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Novel techniques for ground to space quantumRESEARCH channels ◥ transmitting qubits over long distances a truly REVIEW formidable endeavor. Because qubits cannot be copied or amplified, repetition or signalIQC am- @ 2019: plification are ruled out as a means to overcome31 faculty QUANTUM INFORMATION imperfections, and a radically new technological development—such as quantum repeaters157— isGrad students needed in order to build a quantum internet57 Postdoc Quantum internet: A vision (Figs. 2 and 3) (5). We are now at an exciting moment in1800+ time, publications akin to the eve of the classical internet. In late for the road ahead 1969, the first message was sent over the$600M+ nas- funding cent four-node network that was then13 still spin re- -offs 1* 1 1,2 Thomas Jennewein Stephanie Wehner , David Elkouss , Ronald Hanson ferred to as the Advanced Research Projects Institute for Quantum Computing & Department of PhysicsAgency Network (ARPANET). Recent technolog- The internet a vast network that enables simultaneous long-range classical — and Astronomy,ical progress (6–9)nowsuggeststhatwemaysee communication has had a revolutionary impact on our world. The vision of a quantum — the first small-scale implementations of quan- internet is to fundamentally enhance internet technology by enabling quantumUniversity of Waterloo tum networks within the next 5 years. communication between any two points on Earth. Such a quantum internet may operate in [email protected] first glance, realizing a quantum internet parallel to the internet that we have today and connect quantum processors in order to 2020.07(Fig. 3) may seem even more difficult than build- achieve capabilities that are provably impossible by using only classical means. Here, we ing a large-scale quantum computer. After all, we propose stages of development toward a full-blown quantum internet and highlight Downloaded from might imagine that in full analogy to the clas- experimental and theoretical progress needed to attain them. sical internet, the ultimate version of a quantum internet consists of fully fledged quantum com- 1 he purpose of a quantum internet is to include secure access to remote quantum com- puters that can exchange an2 essentially arbi- enable applications that are fundamen- puters (2), more accurate clock synchronization trary number of qubits. Thankfully, it turns out tally out of reach for the classical internet. (3), and scientific applications such as com- that many quantum network protocols do not

A quantum internet could thereby supple- bining light from distant telescopes to improve require large quantum computers to be real- http://science.sciencemag.org/ T ment the internet we have today by using observations (4). As the development of a quan- ized; a quantum device with a single qubit at quantum communication, but some researchers tum internet progresses, other useful applica- the end point is already sufficient for many go further and believe all communication will tions will likely be discovered in the next decade. applications. What’s more, errors in quantum eventually be done over quantum channels (1). Central to all these applications is that a quan- internet protocols can often be dealt with by The best-known application of a quantum in- tum internet enables us to transmit quantum using classical rather than quantum error cor- ternet is quantum key distribution (QKD), which bits (qubits), which are fundamentally differ- rection, imposing fewer demands on the control enables two remote network nodes to establish ent from classical bits. Classical bits can take and quality of the qubits than is the case for a an encryption key whose security relies only on only two values, 0 or 1, whereas qubits can be fully fledged quantum computer. The reason the laws of quantum mechanics. This is im- in a superposition of 0 and 1 at the same time. why quantum internet protocols can outperform possible with the classical internet. A quantum Importantly, qubits cannot be copied, and any classical communication with such relatively

internet, however, has many other applications attempt to do so can be detected. It is this fea- modest resources is because their advantages on December 11, 2018 (Fig. 1) that bring advantages that are unattain- ture that makes qubits naturally well suited for rely solely on inherently quantum properties able with a classical network. Such applications security applications but at the same time makes such as quantum entanglement, which can be Quantum Internet Quantum computing in the cloud: exploited already with very few qubits. By con-Quantum Key Distribution RESEARCH trast, a quantum computer must feature more Fig. 1. Applications of a quantum qubits than can be simulated on a classical com- internet. One application of a quan- puter in order to offer a computational advantage. ◥ tum internet is to allow secure liness and need for a unified frameworkGiven for the challenges posed by the development of REVIEW SUMMARY access to remote quantum com- quantum internet researchers. aquantuminternet,itisusefultoreflectonwhat puters in the cloud (2). Specifically, a capabilities are needed to achieve specific quan-Fixes the loophole of key distribution, where classical keys simple quantum terminal capable of ADVANCES: We define different stagestum of applications and what technology is requiredcould be copied or compromised during transport. QUANTUM INFORMATION preparing and measuring only single development toward a full-blown quantumto realize them. qubits can use a quantum internet to internet. We expect that this classificationHere, we propose stages of developmentOnly transmit single quanta of light per bit. access a remote quantum computer will be instrumental in guiding and assessingtoward a full-blown quantum internet. These experimental progress as well as stimulating Quantum internet:RESEARCHin such| A aREVIEW way vision that the quantum stages are functionality driven: Central to their computer can learn nothing about the development of new applications by provid-definition is not the difficulty of experimentally for the road aheadwhich computation it has performed. ing a common language and reference frameachieving them but rather the essential question Almost all other applications of a quantum internet can be understoodfor the different from two scientific special features and engineering of of what level of complexity is needed to actually Fig. 4. Stagesquantum of quantum entanglement. First, if two qubits at different networkdisciplines nodes are involved. entangled with each enable usefulto attackapplications. the protocol, Each stage and is inter- remains secure at any Stephanie Wehner*, Davidinternet Elkouss, development. Ronaldother, thenHanson suchA entanglement spe- enables stronger than classicalMore correlation advanced and stages coordination. are distinguished For byesting a in itspoint own rightin the and future, distinguished even if by such a a quantum com- cific implementationexample, for of any a measurement quan- on qubit 1, if we made the samelarger measurement amount of function on qubitality, 2, then thus wesupportingspecific quantumputer functionality becomes available that is sufficient later on. This is provably instantaneously obtain the same answer, even though that answer is random and was not to support a certain class of protocols. To illus- ◥ ever more sophisticated Science 362, 303tum (2018) internet may, like for a impossible when using classical communication. BACKGROUND: The internet has had adetermined rev- as secure ahead ofaccess time. to Very remote roughly, quantum it is this comput- feature thatON makes OUR entanglementWEBSITE application so well suited protocols. for trate For this, for each stage we give examples of Alice Bob classical network,tasks that be require optimized coordination. Examples include clock synchronization (3), leader election, and known applicationThe BB84 protocols QKD in which (11) protocol a quantum can be realized by olutionary impact on our world. The vision of ers in the cloud. Read the full article each stage, we describe a quantum internet is to providefor distance, fundamen-achieving functionality, consensusCentral orto about all these data applications (53), or even is the using ability entanglementat http://dx.doi. to help two onlinesome bridge of the players applicationinternet is alreadyusing only known single-qubit to bring advantages. preparations and measure- tally new internet technology by enablingcoordinateof theira quantum actions internet (39). The to second transmit feature quantum of quantumorg/10.1126/ entanglement is thatprotocols it cannot that be are already both. The term network 1 ments tolerating some amount of post-selection p Eve ? shared. If two qubits are maximally entangled with each other,science.aam9288 then it is impossible by the laws of QuTech, Delft University of Technology, Post Office Box L. O. Mailloux et. al. Journal of Cyber Security and Information quantum communicationcommonly between any refers two tobits a (qubits) situation that are fundamentally different known and that can5046, be 2600Downloaded from GA Delft, Netherlands. 2Kavli Institute of quantum mechanics for a third qubit to be just as entangled...... with either of them. This makes (19). For known protocols in this stage, eT + eM ≤ Systems, 4, 2 – Basic Complexity points on Earth. Such a quantumthat goes internet beyond point-to-pointthan classical bits. Whereas classical bits can realized with the func-Nanoscience, Delft University of Technology, Post Office Box will—in synergy with the “classical” internetentanglementtake only inherently two values, private, 0 bringing or 1, qubits great can advantages be in totionality tasks that provided require securityin that suchstage. as It is con-5046, 2600 GA0.11 Delft, is Netherlands. sufficient and can be estimated by testing that we have today—connectcommunication; quantum infor-generating thea superposition encryption objective keys of of (12 being) or secure0 and 1 identification at the same (24,ceivable25). that a simpler protocol, or better*Correspondingfor author. only Email: a [email protected] number of states (20). In practice, mation processors in ordera to network achieve unpar- is to providetime. Moreover, any end qubits can be entangled with theoretical analysis, may be found in the fu- single-qubit preparationcanbereplacedwithat- alleled capabilities that are provablynodes impossible (connectedWehner eteach to al.,the Science other,362 leading, eaam9288 to correlations (2018) 19 overOctober large 2018 ture that solves the same task but is less de- tenuated laser pulses, using1 of also 9 decoy-state BB84

by using only classical information.network) with thedistances means to that exchange are much data, stronger making than is three pos- endmanding nodes in the terms smallest of functionality. instance In of parallel a true http://science.sciencemag.org/ to guarantee security (21). QKD is commercially As with any radically new technology, it is sible with classical information. Qubits also to the daunting experimental challenges in network. Outside the laboratory, only trusted repeater networks (first stage) have been realized in available at short distances by using standard 10 hard to predict all uses of the future quantum cannot be copied, and any attempt to do so making quantum internet a reality, there is 11 internet. However, several majormetropolitan applications areascan (62– be65 detected.).Two single This feature far-away makes end qubits nodes (68thus) have an opportunity also been connected for quantum via software satellite. telecom fibers (22), and a variety of protocols are have already been identified, including secure well suited for security applications but at the developers to design protocols that can realize known [(23), survey]. communication, clock synchronization, extend- same time makes the transmission of qubits ataskinastagethatcanbeimplemented Another class of protocols in this stage is in the ing the baseline of telescopes,So secure far, most identi- applicationrequire radically protocols new conceptshave only and technol-other interestingmore easily. tasks. We identify Informally, relevant parameters this stage domain of two-party cryptography. Here, there is fication, achieving efficient agreement on ogy. Rapid experimental progress in recent for each stage to establish a common language distributed data, exponentialbeen savings analyzed in com- foryears perfect has broughtparameters. first rudimentary As such, quantumallows anybetween node hardware to prepare and software a one-qubit developers. state no eavesdropper, but rather Alice and Bob them- munication, quantum sensorthe networks, exact as requirements well networks of within many reach, application highlighting theand time- transmitLast, we the review resulting technological state progress to any in other ex- selves do not trust each other. An example of such Downloaded from protocols on these parameters have not yet been node, whichperimental then physics, measures engineering, it (definition and comput- is a task is secure identification, in which Alice

determined and deserve future investigation. Al- provideder sciencein Table that 1).is required Transmission to attain such and stages. mea- on December 11, 2018 (a potentially impersonating user) may wish to 1 though functionality-driven stages make de- surementOUTLOOK: are allowedBuilding to be and post-selected; scaling quantum that identify herself to Bob (a potentially malicious mands on the communication links and quantum is, a signalnetworks that is the a formidable qubit is endeavor, lost may requiring be gen- server or automated teller machine) without re- repeaters, it will not be important in this sec- erated instead.sustained For and instance, concerted the efforts receiving in physics, node vealing her authentication credentials (24, 25). It tion how these links are realized; they may be is allowedcomputer to ignore science, nondetection and engineering events to suc- and is known that even by using quantum communi- ceed. The proposed stages of development

realized by direct transmission in fiber, by being conclude that such qubits are lost. If the sen- cation, such tasks cannot be implemented secure- http://science.sciencemag.org/ will facilitate interdisciplinary communica- relayed by any kind of quantum repeater, or der cantion prepare by summarizing an entangled what state we of may two actually qubits, ly without imposing assumptions on the power of even by means of teleportation using preshared then thiswant stage to achieve also and includes providing the guidelines special both case the adversary (26–28). Classical protocols rely on entanglement. What matters is that these links in whichto the protocol sender design transmits and software the development first and se- computational assumptions, whose security against can be used to generate the necessary quantum cond qubitas well to two as hardware different implementations nodes in the through network an attacker who holds a quantum computer is states for a specific stage. (or to anotherexperimental node physics and itself). and engineering. Such entangle- Al- unclear. Nevertheless, it is possible to achieve though it is hard to predict what the exact ment distributioncomponents ofis athen future also quantum post-selected. internet will provable security for all such relevant tasks by Trusted repeater networks Such abe, post-selected it is likely that prepare-and-measure we will see the birth offunc- the sending more qubits than the adversary can store The first stage differs substantially from the tionalityfirst isnot multinode equivalent quantum to networks transmitting in the next arbi- easily within a short time frame, which is known others in the sense that it does not allow the trary qubitsfew years. across This the development network (18 brings). The the task ex- of as the bounded (29)ormoregenerallynoisy- end-to-end transmission of qubits. Nevertheless, transmittingciting arbitrary opportunity qubits to test demands all the ideas the and abil- storage model (30, 31). This assumption only functionalities that so far only exist on paper

from a technological perspective, trusted re- ity to transfer an unknown state Y (which the needs to hold during the execution of the proto- on December 11, 2018 and may indeed be the dawn ofj ai future large- peater networks can form an interesting stepping sender doesscale not quantum know internet. how to prepare) determinis- col, and security is preserved into the future even stone toward a quantum internet, spurring in- tically to the receiver—that is,▪ no post-selection on if the adversary later obtains a better quantum frastructure deployment and engineering devel- detection events is allowed. memory. There exist protocols for which it is suf- Stages in the developmentopments; of a quantum depending internet. onEach the underlying stage is characterized technology, by an The classical reader may wonder what is the ficient to prepare and measure single qubits, in increase in functionality at the expense of greater technological difficulty. This Review provides a The list of author affiliations is available in the full article online. trusted repeaters (10) can be upgraded to true use of transmitting*Corresponding author. qubits Email: [email protected] at all if there is a which the sufficient values of p, eM, eT (Table 1) clear definition of each stage,quantum including benchmarks repeaters and later examples on. of known applications, andprocedureCitefor this article the sende as S. Wehnerr toet prepare al., Science the362, state eaam9288Y . depend on the storage assumption (32). provides an overview of the technological progress required to attain these stages. (2018). DOI: 10.1126/science.aam9288 Specifically, a trusted repeater network (some- After all, we might imagine that the sender sim-j i Other known protocols in this stage include times called a trusted node network) has at ply sends classical instructions for this procedure position verification (33); weakened forms of two- Wehner et al., Science 362, 303 (2018)least two 19 October end 2018 nodes and a sequence of short to the receiver, who then prepares the qubit1 of 1 it- party cryptographic tasks that can form building distance links that connect nearby intermediary self. The difference between such a classical pro- blocks, such as imperfect bit commitments (34); repeater nodes. Each pair of adjacent nodes tocol and sending different quantum states Y and coin-flipping (35). Here, the requirements in j i uses QKD (11–13) to exchange encryption keys. directly is that in the latter case, an eavesdropper, terms of p, eM,andeT have not been analyzed yet; These pairwise keys allow the end nodes to or indeed the receiver, cannot make a copy of Y no task exists for which a full set of necessary generate their own key, provided that all inter- without disturbing the quantum state. This meansj i and sufficient conditions on these parameters is mediary nodes are trusted (14). A first step that attempts to gain information from Y by an known. toward upgrading such networks could be mea- eavesdropper may be detected, enablingj QKD.i surement device–independent QKD (15–17), which Entanglement distribution networks is a QKD protocol that is secure even with un- Application protocols The third stage allows the end-to-end creation trusted measurement devices that can be im- This stage is already sufficient to realize proto- of quantum entanglement in a deterministic or plemented with standard optical components cols for many interesting cryptographic tasks, heralded fashion, as well as local measurements. and sources (17); this protocol already incor- as long as the probability of loss (p)andthein- The end nodes require no quantum memory for porates some useful ingredients for later stages, accuracies in transmission (eT) and measure- this stage (Table 1). such as two-photon Bell measurements. ment (eM)(Table1)aresufficientlylow.Themost The term “deterministic entanglement gener- famous of such tasks is QKD, which provides a ation” refers to the fact that the process succeeds Prepare and measure networks solution to the task of generating a secure en- with (near) unit probability. Heralding is a slight- This stage is the first to offer end-to-end quan- cryption key between two distant end nodes ly weaker form of deterministic entanglement tum functionality. It enables end-to-end QKD (Alice and Bob) (11–13). QKD is secure even if the generation in which we signal the successful gen- without the need to trust intermediary repeater eavesdropper trying to learn the key has access to eration of entanglement with an event that is in- nodes and already allows a host of protocols for an arbitrarily large quantum computer with which dependent of the (immediate) measurement of the

Wehner et al., Science 362, eaam9288 (2018) 19 October 2018 3 of 9 7/31/20

Historical note on QKD

VOLUME 84, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 15 MAY 2000

Quantum Cryptography with Entangled Photons VOLUME 84, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 15 MAY 2000 Thomas Jennewein,1 Christoph Simon,1 Gregor Weihs,1 Harald Weinfurter,2 and Anton Zeilinger1 1Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria 2 Sektion Physik, Universität München, Schellingstrasse 4͞III, D-80799 München, Germany [9] C. H. Bennett, F. Bessette, G. Brassard, L. Savail, and J. (Received 24 September 1999) Smolin, J. Cryptol. 5, 3 (1992); A. Muller, J. Breguet, and By realizing a quantum cryptography system based on polarization entangled photon pairs we establish N. Gisin, Europhys. Lett. 23, 383 (1993); J. D. Franson and highly secure keys, because a single photon source is approximated and the inherent randomness of B. C. Jacobs, Electron. Lett. 31, 232 (1995); W. T. Buttler, quantum measurements is exploited. We implement a novel key distribution scheme using Wigner’s R. J. Hughes, P.G. Kwiat, S. K. Lamoreaux, G. G. Luther, inequality to test the security of the quantum channel, and, alternatively, realize a variant of the BB84 G. L. Morgan, J. E. Nordholt, C. G. Peterson, and C. M. protocol. Our system has two completely independent users separated by 360 m, and generates raw keys Simmons, Phys. Rev. Lett. 81, 3283 (1998). at rates of 400–800 bits͞s with bit error rates around 3%. [10] C. Marand and P.D. Townsend, Opt. Lett. 20, 1695 (1995); PACS numbers: 03.67.Dd, 42.79.Sz, 89.80.+h R. J. Hughes, G. G. Luther, G. L. Morgan, C. G. Peterson, and C. Simmons, Lect. Notes Comput. Sci. 1109, 329 The primary task of cryptography is to enable two par- In any real cryptography system, the raw key generated (1996); A. Muller, T. Herzog, B. Huttner, W. Tittel, H. ties (commonly called Alice and Bob) to mask confidential by Alice and Bob contains errors, which have to be cor- messages, such that the transmitted data are illegible to any rected by classical error correction [7] over a public chan- Zbinden, and N. Gisin, Appl. Phys. Lett. 70, 793 (1997). unauthorized third party (called Eve). Usually this is done nel. Furthermore, it has been shown that whenever Alice [11] N. Lütkenhaus, G. Brassard, T. Mor, and B. C. Sanders (to using shared secret keys. However, in principle it is always and Bob share a sufficiently secure key, they can enhance be published). possible to intercept classical key distribution unnoticedly. its security by privacy amplification techniques [8], which [12] One photon of the pair can be used as a trigger for finding The recent development of quantum key distribution [1] allow them to distill a key of a desired security level. the other photon of the pair, provided that the probability can cover this major loophole of classical cryptography. It A range of experiments have demonstrated the feasi- FIG. 3 (color). The 49984 bit large keys generated by the of producing two pairs at a single time can be neglected. allows Alice and Bob to establish two completely secure bility of quantum key distribution, including realizations BB84 scheme are used to securely transmit an image [23] (a) P. Grangier, G. Roger, and A. Aspect, Europhys. Lett. 1, keys by transmitting single quanta (qubits) along a quan- using the polarization of photons [9] or the phase of pho- of the “Venus von Willendorf” [24] effigy. Alice encrypts the 4 (1986); 1, 173 (1986); J. G. Rarity, P.R. Tapster, and E. tum channel. The underlying principle of quantum key dis- tons in long interferometers [10]. These experiments have image via bitwise XOR operation with her key and transmits the Jakeman, Opt. Commun. 62, 201 (1987). tribution is that nature prohibits gaining information on the a common problem: the sources of the photons are attenu- encrypted image (b) to Bob via the computer network. Bob de- [13] Note also that in our case the beam splitter attack is less state of a quantum system without disturbing it. Therefore, ated laser pulses which have a nonvanishing probability to crypts the image with his key, resulting in (c) which shows only a few errors due to the remaining bit errors in the keys. effective than for coherent pulses, because even when two in appropriately designed schemes, no tapping of the qubits contain two or more photons, leaving such systems prone pairs are produced simultaneously, Eve does not gain any is possible without showing up to Alice and Bob. These to the so-called beam splitter attack [11]. In this Letter we presented the first full implementa- information in those cases where Alice and Bob detect pho- secure keys can be used in a one-time-pad protocol [2], Using photon pairs as produced by parametric down- tons belonging to the same pair, because then the photon which makes the entire communication absolutely secure. conversion allows us to approximate a conditional single tion of entangled state quantum cryptography. All the detected by Eve originates from a different pair and is com- Two well-known concepts for quantum key distribution photon source [12] with a high bit rate [13], and yet a very equipment of the source and of Alice and Bob has proven are the BB84 scheme and the Ekert scheme. The BB84 low probability for generating two pairs simultaneously. pletely uncorrelated to Alice’s and Bob’s photons. to operate outside shielded lab environments with a very [14] P.R. Tapster, J. G. Rarity, and P.C. M. Owens, Phys. Rev. scheme [1] uses single photons transmitted from Alice to Moreover, when utilizing entangled photon pairs one im- high reliability. While further practical and theoretical in- Bob, which are prepared at random in four partly orthog- mediately profits from the inherent randomness of quantum Lett. 73, 1923 (1994); W. Tittel, J. Brendel, H. Zbinden, 12 vestigations are still necessary, we believe that this work 13 onal polarization states: 0 ±, 45 ±, 90 ±, and 135 ±. If Eve mechanical observations leading to purely random keys. and N. Gisin, Phys. Rev. Lett. 81, 3563 (1998); G. Weihs, tries to extract information about the polarization of the Various experiments with entangled photon pairs have demonstrates that entanglement based cryptography can be T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, photons she will inevitably introduce errors, which Alice already demonstrated that entanglement can be preserved tomorrow’s technology. Phys. Rev. Lett. 81, 5039 (1998). and Bob can detect by comparing a random subset of the over distances as large as 10 km [14], yet none of these This work was supported by the Austrian Science [15] E. P. Wigner, Am. J. Phys. 38, 1005 (1970). generated keys. experiments was a full quantum cryptography system. We Foundation FWF (Projects No. S6502, No. S6504, and [16] M. Zukowski (private communication); L. C. Ryff, Am. J. The Ekert scheme [3] is based on entangled pairs and present in this paper a complete implementation of quan- No. F1506), the Austrian Academy of Sciences, and Phys. 65, 1197 (1997). uses Bell’s inequality [4] to establish security. Both Al- tum cryptography with two users, separated and inde- the IST and TMR programs of the European Commis- [17] C. H. Bennett, G. Brassard, and N. D. Mermin, Phys. Rev. ice and Bob receive one particle out of an entangled pair. pendent of each other in terms of Einstein locality and Lett. 68, 557 (1992). sion [Contracts No. IST-1999-10033 (QuComm) and They perform measurements along at least three different exploiting the features of entangled photon pairs for gen- [18] P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. directions on each side, where measurements along paral- erating highly secure keys. No. ERBFMRXCT96-0087]. Sergienko, and Y.H. Shih, Phys. Rev. Lett. 75, 4337 lel axes are used for key generation and oblique angles are In the following, we will describe the variants of the (1995). used for testing the inequality. In Ref. [3], Ekert pointed Ekert scheme and of the BB84 scheme, both of which [19] T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and out that eavesdropping inevitably affects the entanglement we implemented in our experiment, based on polarization between the two constituents of a pair and therefore re- entangled photon pairs in the singlet state A. Zeilinger, Rev. Sci. Instrum. (to be published). duces the degree of violation of Bell’s inequality. While [1] C. H. Bennett and G. Brassard, in Proceedings of the In- [20] S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, 2 1 we are not aware of a general proof that the violation of a C ͘ ෇ ͓H ͘A V͘B 2 V͘A H ͘B͔, (1) ternational Conference on Computer Systems and Signal Appl. Opt. 35, 1956 (1996). Bell inequality implies the security of the system, this has j p2 j j j j Processing, Bangalore, 1984, p. 175; C. H. Bennett, G. [21] Note that it would be simple to bias the frequencies of been shown [5] for the BB84 protocol adapted to entan- where photon A is sent to Alice and photon B is sent Brassard, and A. Ekert, Sci. Am. 267, 26 (1992). analyzer combinations to increase the production rate of gled pairs and the Clauser-Horne-Shimony-Holt (CHSH) to Bob, and H and V denote the horizontal and vertical [2] In this classical cryptographic protocol the message is com- the keys. inequality [6]. Why Satelliteslinear polarization, for respectively.Long This state Distance shows perfect bined withQ a random-Com? key string of the same size as the [22] Removal of one bit erases the information about the blocks message to form an encoded message which cannot be de- contained in the (public) parities. Quantum Communication in Space 0031-9007͞00͞84(20)͞4729(4)$15.00 © 2000 The American Physical Society 4729 ciphered by any statistical methods. G. S. Vernam, J. Am. [23] Windows-BMP format containing 60 3 90 pixels, 8 bit Inst. Electr. Eng. 55, 109 (1926). color information per pixel: 43 200 bit of picture infor- [3] A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991). mation. The file includes some header information and a IdQuantique Commercial QKD System [4] J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1965). color table, making the entire pictureDedicated file 51 840 bit. We en- quantum hardware in Space: • Ground-based [5] C. Fuchs, N. Gisin, R. B. Griffiths, C. S. Niu, and A. Peres, crypted only the picture information, leaving the file header • Phys. Rev. A 56, 1163 (1997). and the color table unchanged.• China (J.W. Pan) Practical systems typically 100 km [6] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, [24] The “Venus” von Willendorf was found in 1908 at Wil- • Demonstrations up to to 400 km Phys. Rev. Lett. 23, 880 (1969). lendorf in Austria and presently resides• Entanglement in the Naturhis- Distribution over 1200 km ! (Science, 2017) [7] C. H. Bennett and G. Brassard, J. Cryptol. 5, 3 (1992). torisches Museum, Vienna. Carved from limestone and • Optic fibre loss 0.15 dB/km at best [8] C. H. Bennett, G. Brassard, C. Crépeau, and U. M. Maurer, dated 24 000–22 000 BC, she represents• anQKD, icon of prehis-Teleportation (Nature 549, 43–47 and 70-73 (2017) IEEE Trans. Inf. Theory 41, 1915 (1995). toric art. • Free-space limited due to line-of-sight • QKD between Bejing and Graz (PRL), QKD using Bell-pairs

• Commercial Devices available: 4732 (CLEO 2019, Nature2020) • Note: Optical amplifiers not possible! • Japan (NICT) • 50 kg satellite: Nature Photonics 11, 502–508 (2017) • Longer distances: • Singapore (A. Ling) • Trusted Repeaters • Correlated Photon Source onboard CubeSat (> 2000km network China) (Phys. Rev. Applied 5, 054022, 2016) • Long lifetime Quantum Memories • SpooQey-1: July 2019: Entanglement in space • Quantum Repeaters Beijing and Vienna have a quantum conversation • Satellites Takesue et al, Nature Photonics 1, 2W(L) September 2017, www.physicsworld.com 343 - 348 (2007) 2W0 • Several more missions in preparation http://english.cas.cn/newsroom/news/201709/t20170928_1 Ma, Fung, Lo, Phys. Rev. A 76, 83577.shtml 012307 (2007) 14 19

2 7/31/20

And was noticed by the world! Canadian Quantum Satellite

http://www.asc- csa.gc.ca/eng/sciences/qeyssat.asp

In the section Pioneers. Announced April, 2018.

Minister Bains, April 2017 20 21

Modeling the performance of satellite QEYSSat will be a Technology Demonstration Platform to ground quantum6 link

0.8 405 nm • Optimized Quantum Receiver 532 nm 0.7 670 nm 785 nm • Analysis of wavelengths with windows of 830 nm • 0.6 1060 nm Multiple partners across Canada ‘good’ atmospheric transmission 1550nm 13 • 4 0.5 Transmitter telescopes are ‘compact’ • Link modelled using turbulence; Table 1. Calculated length of distributed cryptographic key for various • 0.4 Networking with fiber optics H diffraction to account for beam wavelengths with a WCP (left) and an entangled photon (right) source. Of the Receiver Transmittance • laser-line wavelengths studied, 670 nm produces the longest key for a downlink, 0.3 Test link with various quantum sources http://www.spaceq.ca/honeywell-aerospacePower-wins-301m-million-contract-to-build-qeyssat-satellite/ obstruction; background signals while 785 nm produces the longest key for the uplink. Downlink is with a 10 cm Input from Fiber optics meter MM transmitter and a 50 cm receiver; uplink is with a 50 cm transmitter and a 30 cm 0.2 • Study of quantumBob’s link and PBS V receiver. Simulations are of the upper quartile satellite pass (in terms of pass PBS PC 0.1 telescope H 1m Laser duration) with a 600 km orbit, pointing error of 2 µrad and rural atmosphere entanglement science PBS Trusted Relay North America – the cutout is centred around Ottawa (5 km visibility) at sea level. Source rate: 300 MHz for WCP and 100 MHz MM 808nm 0 V for entangled photon source; detector dark count rate: 20 cps; detection time 10 20 30 40 50 60 70 80 90 D 18 Angle from the horizon [degree] Receiver window: 0.5 ns. • Multiple ground stations in Canada, D 2m MM BS FigureSecure key length obtained 2. Simulated for the upper quartile satellite atmospheric pass (kbit) transmittance at a typical rural location, for Pinhole Coupling A and around the globe 90:10 R:T Wavelength Downlink,propagation WCP Uplink, WCP at Downlink, zenith entangled (left) Uplink, entangled and for different elevation angles (right). Coloured lens A (nm) source source photon source photon source Rotated 45˚ BS lines represent wavelengths of commercially available laser systems. Several • Research on ground station 405 68.5 3.5 6.2 0 Location B 532 264.5transmission 33.1 windows 119.3 are 12.1 evident, within which optical transmission would capabilities such as AO or different Location A FIG. 4. Setup for measuremente.g. Waterloo of the reverse propagation 670 465.6experience 87.7 low loss.324.7 Generally, 67.4 the transmission tends to be better at higher e.g. Calgary loss and polarisation extinction ratio. An 808 nm laser is con- 785 458.3wavelengths, 111.3 but 272.9 other factors 75.7 (e.g. diffraction, sources and detectors) must be quantum emitters, etc. Bob 830 317.3 82.1 136.1 39.7 nected to each of the output channels of the receiver, one at a 1060 175.4taken into 67.6 account 21.8 to properly 8.1 determine the best wavelength choice. time. A 90:10 reflection:transmission (R:T) ratio beamsplit- 1550 123.9 94.8 12.8 14.4 Alice ter diverts the reverse propagating beam to the measurementM. Toyoshima, op.Ex. 2011 error can be averaged over timeRelated as analysis: additional beam broadening. Controlling for jitter is more challenging on a satellite, thus aJ. Rarity downlink et al, NJP, 2002 will be more vulnerable to this effect. The pointing unit. The latter consists of a fiber-coupled optical power me- J.P. BourgoinWe further, et al, assume NJP, that 15:023006, only half of the 2013 nights have clear skies,P. Villoresi automaticallygroup, NJP, 2009 rendering half R. Ursin group, NJP, 2013 ter, and a rotating PBS to measure power and polarization Figure B.1. Light pollution from human activities in North America, data from accuracythe passes unusable must due be to cloud better coverage. than Actual cloud the coverage combined will depend on the beam ground waist from diffraction and turbulence to avoid extinction ratio of the reverse propagation beam. A polar- World Atlas of Artificial Sky Brightness [72]. The inset shows a closer view of becomingstation location a ultimately dominant chosen. The source average global of cloud loss. coverage on land is between 50 the location of the simulated ground site, marked with a cross, approximately andTransmittance 90%, with over 25% of clouds through having a thin density atmosphere [63]. Many areas, particularly is dependent in drier on both wavelength (see figure 2, left) and ization controller PC is used to maximize throughput power 20 km outside Ottawa. angleor more (figure elevated regions,2, right), experience less and than 20% is cloud a result cover, some of having the near 0% types cloud and concentrations of molecules and particles 23 from each receiver channel. 29 cover [64]. A location with 50% cloud coverage would likely represent a worst case of any site Appendix B. Estimating background light thatthat are would present. be reasonably considered. Several low-loss transmission windows can be found—most notable are those at 665–685,The results show 775–785, that a downlink can generate1000–1070 more secure key bits and than an 1540–1680 uplink for the nm, all of which support wavelengths of Background light originates from both natural and artificial sources. Natural sources, such as the Sun, Moon and stars, have been thoroughly characterized elsewhere. Artificial sources consist commercialsame ground and satellite laser telescopes. diodes. Furthermore, Using the WCP source MODTRAN outperforms the entangled 5 [48], we model atmospheric transmittance of TABLE I. Reverse propagating extinction ratio measurement largely of light pollution from human activities. Shown in figure B.1, this light pollution was a ruralphoton sea-level source, due in part to location the higher source with rate for WCP, avisibility and in part to the inefficiency of 5 km,of chosen to approximate ground stations near of Bob’s setup. The photons from H and V channel could characterized over the surface of the Earth during 1996 and 1997 by the Defence Meteorological largedetecting cities the transmitter’s (such heralding stations photon in the could entangled source. be utilized A downlink with to a satellite connect city-wide QKD networks globally). FIG. 3. Receiver designed by INO working as a passive basis Satellite Program’s (DMSP) Operational Linescan System (OLS) [71]. We utilize these light transmitter telescope as small as 10 cm and a receiver of 50 cm could be used to successfully choice polarization analyzer at 785 nm. Top: the important be distinguished with high probability. The measured pollution data for our calculations. exchangeOur a key numerical of 4.5 Mbit per month model with an entangled incorporates photon source and 25 Mbit all perthe month aforementioned loss contributions, as well as extinction ratios of A and D channels are low, presumably (wavelengthwith a WCP source. dependent) In an uplink, a 30 cm receiver scattering telescope on the and satellite absorption and a ground losses due to receiver optical components optical components consists of a pinhole, coupling lens, beam- B.1. Downlink owing to polarization becoming elliptical at reflections in the andtransmitter detectors, of at least 25 to cm determinecould produce 0.4 Mbit the key per expected month with an entangled key photon rates. Diffraction is simulated by discretizing the splitter (BS), and polarizing beamsplitters (PBSes). Bottom: A receiver which is located at a ground station will receive light from bright objects in the sky transmissionsource and 3 Mbit per beam month with aintensity WCP source. profile into a 50 50 grid. A radial intensity profile comprising photo of the receiver. Four multimode fibers lead to the four measurement unit. (e.g. stars) and from scattered light originally emitted by human activities. Astronomers have 5000 samplesInterestingly, for an spanning uplink, varying the size 50 of them ground from transmitter the telescope centre has little⇥ of the receiver is then calculated following characterized the natural brightness of the night sky at different locations [73–75]. Theoretical effect on the number of key bits generated. This is because, for a transmitter telescope of 25 cm 3 detectors (not shown). models and computer algorithms to predict the night sky brightness also exist [76]. The Rayleigh–Sommerfeldor more, turbulence dominates the beam divergence, diffraction limiting any gains as that propagated could otherwise be from each point of the transmission profile Output max min Extinction contribution of the Moon to the night sky brightness has been studied [77]. grid.found This by reducing discretization diffraction via increasing the allows transmitter telescope us to diameter. model our final beam profile for a wide range of beam The nighttime sky brightness due to light pollution can be calculated from the DMSP-OLS We also determine the long-distance performance of two other important quantum channel Angle Power Angle Power ratio data which specify the measured upward flux emitted at a given ground location [78]. Since the waists, shapes and telescope designs. Pointing error and atmospheric turbulence (in the case of experiments: Bell tests and quantum teleportation. For both experiments, we analyse each (deg) (µW) (deg) (µW) ground-based telescope is pointing towards a satellite, it can receive background counts from an uplink) are added using a two-dimensional convolution between the calculated diffraction prevent spatial mode attack [25], focusing lens to focus the Sun’s light reflecting off the satellite and into the telescope. For our case we will assume the profilesatellite and pass independently the Gaussian to determine whichdistribution pass can perform a successful of Bell pointing test or error and turbulence. The final intensity H325.0910.15167 satellite is not illuminated by the Sun. (For our orbit, this will be valid for all nighttime passes incoming beam into optical fibers, and an integrated op- at most ground station locations.) The overall sum of these contributions amounts to the total profileNew Journal is of Physics integrated15 (2013) 023006 (http://www.njp.org/ over the) receiving area to determine the received power (proportional tics module. The latter consists of a beamsplitter (BS) V9419.810.03660 number of background counts per second (per nm of filter bandwidth): to the probability of receiving each photon). We then add the remaining loss contributions 1 2 2 Ntot (Hnat + Hart) ⇥(FOV) ⇥r , (B.1) (atmospheric and optical transmissions, detector efficiency). For details, see appendix A. to passively select the basis of measurement and PBSes D 315 20.7 223 1.94 10.7 = E0 ⇥ in each basis to discriminate the four polarizations of the A4923.51413.696.4 New Journal of Physics 15 (2013) 023006 (http://www.njp.org/) New Journal of Physics 15 (2013) 023006 (http://www.njp.org/) incoming photons: horizontal (H), vertical (V), diagonal (D), and antidiagonal (A). We have done measurements on this receiver to characterize the backflash emission as values lie in the range 0.088 to 0.094). Assuming back- a possible side channel attack. flash photons are randomly polarized, their transmission should be approximately half of this upper bound. Next, we demonstrate Eve’s ability to distinguish the A. Reverse loss and extinction ratio originating channel of backflash photon. For that, we measure polarization extinction ratio of the reverse emit- As the photons back-propagate through the setup, ted beam from the receiver. In Fig. 4, a 90:10 reflec- they experience the reverse loss of the receiver, i.e., the tion:transmission (R:T) ratio beamsplitter is added to loss from originating detector to the channel input. This divert the outgoing beam from the receiver to a mea- could reduce probability that backflash photon leaks into surement unit consisting of a PBS and a fiber-coupled the channel. The setup shown in Fig. 4 is used to esti- optical power meter. This additional setup has through- mate this loss. An 808 nm laser (wavelength close to put eciency Te =0.60. For each receiver channel input, the operating wavelength of the receiver) is connected to we rotate the PBS to find a pair of angles that results the receiver’s output multimode fiber, one channel at a in maximum and minimum power at the power meter. time. We adjust the polarization controller PC to max- The optimal angles for each channel and respective ex- imize throughput power, providing an upper bound of tinction ratios are shown in Table I. The drastically lower the reverse transmission. The laser power at the end of extinction ratio in D and A polarization is likely a result receiver’s fiber is P1 = 40 µW. We then measure laser of polarization distortion caused by Fresnel e↵ect on the power P2 emitted at the front of the receiver module. dielectric mirror and the 90:10 BS used by Eve. These The reverse transmission eciency of the receiver for the reflective surfaces were aligned at a certain angle along optimum polarization is then Tb = P2/P1. We have mea- the axis corresponding to V polarization. This alignment sured the average reverse transmission eciency over all distorted the diagonal polarization of the reflected beam, four channels of this receiver T 0.091 (the individual by inducing a phase di↵erence between its H and V po- b ⇡ 7/31/20

QEYSSat Payload Prototype Full quantum receiver optics Ground to Aircraft Demonstration

• Fully functional form-representative quantum-payload • Components have ‘path to flight’ • Projected mass: ~ 23 kg, Power <30W, envelope ~ 60cm^3 • Tests: Radiation, TVAC, aircraft link

Payload detectors and electronics

C. Pugh et al., Quantum Science and Technology, 2017; 2 (2): 024009

Press release: https://uwaterloo.ca/institute-for-quantum-computing/news/iqc- advances-quantum-satellite-mission

34 36

Airborne QKD tracking system • Airborne Trials 2016- Sep. 20 / 21 Novel Protocols for Free-Space • Night #1: 7 passes, of which 2 acquired Quantum Communications signal. Night #2: 8 passes, of which 5 acquired signal. • 3 km line pass: secure key (finite size Lessons learnt from previous tests included) of 46805 bit, 35 seconds. 3km pass: • 10 km arc pass: - Reference Frame Independent QKD secure key (finite size included) 41899 bit, - Alternative Encoding of Photonic Qubits 250 seconds. - HOM Interference with Structured Pulses

C. Pugh et al, Quantum Science and Technology, 2, 2, 024009 (2017) 37 38

4 Demonstration of a Reference Frame Independent channel for Quantum Key Distribution 6-4 State Protocol

1, 1 1 1 1 1, 2 Ramy Tannous, ⇤ Zhangdong Ye, Jeongwan Jin, Katanya B. Kuntz, Norbert Lütkenhaus, and Thomas Jennewein 1Institute for Quantum Computing, Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada 2Quantum Information Science Program, Canadian Institute for Advanced Research, Toronto, Ontario, M5G 1Z8 Canada (Dated: May 16, 2019) We propose and report the experimental results of a novel protocol for reference frame independent quantum key distribution using six states for Alice and four states for Bob. We show that this protocol is reference frame independent despite the reduced four-state measurement in Bob’s polarization state analyzer. We perform a proof-of-principle experiment using polarization entangled photon pairs. Despite a rotational phase, we obtain a consistently low error rate of less than 3% indicating the feasibility of this protocol for quantum key distribution. Our protocol is beneficial but not limited to applications in satellite or mobile free-space QKD, where the remote communication node can save resources and simplify the setup by restricting the number of measured states to four instead of six. 2 INTRODUCTION: TABLE I: Polarization basis with the corresponding Pauli where M is the expectation value of the two qubit positive- converted photons are then collected into PMF’s with the hor- h spini matrix. The symbols used in this work are in the last Quantum key distribution (QKD) protocols provideoperator a valued measure (POVM)column.M, defined as, izontal and vertical polarizations aligned to the two principle means of generating and sharing an encryption key between axes, (slow and fast axis), of the PMF. Thus, the horizontal M++ M+ M + + M two parties, Alice and Bob, with the security guaranteed by M = . (2) and vertical polarizations are preserved while any other po- Basis Pauli Spin Operator Symbol the laws of quantum physics [1]. There is an on-going ef- h i ÂijMij larization incident on the fiber will have a random rotational H/V sz Z fort to improve the practicality and robustness of QKD [1]. In D/A s X phase due to the difference in index of refraction between the Mij (i, j =+, ) are the coincidencex counts of the various many protocols, both Alice and Bob need continuous agree- R/L sy Y slow and fast axis. The axes also differ in group velocity and results for the POVM M and  Mij is the total coincidence ment of all shared measurement frames during the entire pe- ij thus the slow and fast component fo the polarization will be counts measured of M. By Pauli algebra, we see that C 1, riod of communication [2–4]. The definition of the measure-  temporally displaced after traversing the PMF. We call this ment frames is essential for key generation, for instance proto-with the equality occurring for maximally entangled states. information purposes despite the rotational phase that is in- displacement the walk-off. cols that utilize polarization encoding, a geometric referenceTherefore, the C-parameter effectively provides a second ba- duced to superposition bases. is required. However, this demandUnstructured can be relaxedUnstructured by employ- quantumsis that quantum can key be useful distribution key indistribution a quantum communication context, The entangled photons travel through 2 m of 780 nm PM ing reference frame independent protocols (RFI), that allowsand will be called the "diagonal*" basis. The C value is used fibers and which are rotated by 90 relative to one another. all or some of the measurementUnstructuredUnstructured framesPatrick to freely J. toColes, rotate quantum quantum Ericto by monitor M. keyMetodiev, key the distribution quality distribution and of Norbert the quantum Lütkenhaus channel and any signif- The equality of the lengths of the fibers is critical since the Patrick J.Unstructured Coles, Eric M. quantum Metodiev, keyand distributionNorbert LütkenhausProtocol 7/31/20 some slowly varyingInstitute relative phase[5–7] forInstitute Quantumf for. RFI ComputingQuantum protocols Computing areandicant Department drop and from Department unity of Physics can of Physics be and attributed Astronomy, and Astronomy, to an eavesdropper’s walk-off induced to Alice’s photons should be the same for University of Waterloo, N2L3G1 Waterloo, Ontario, Canada useful in many settings suchPatrickUnstructuredPatrick asUniversity free-space J. J.Unstructured Coles, Coles, ofsatellite Waterloo, Eric linksquantum M. M. where Metodiev,quantum N2L3G1 Metodiev,intervention[5]. key Waterloo, and keyand distribution Norbert NorbertdistributionC is Ontario, a Lütkenhaus statistical Lütkenhaus Canada value and it can be shown to Bob’s photon. The walk-off must be less than the pump’s co- Institute forPatrick Quantum J. Coles, Computing Eric M.and Metodiev, DepartmentFor andthe of 6-4 Physics Norbert RFI QKD and Lütkenhaus Astronomy, protocol, we modify the scheme pre- the frames of referenceInstitute mayQuantumInstitute not for be Quantum maintained for key Quantum distribution Computing due Computing to (QKD) rotations andbe allows and constant Department Department for communication even of ofin Physics Physicsthe betweenpresence and anddistant Astronomy, Astronomy, of a relative parties with phase security between herence time, since the coherence time of the entangled pho- University of Waterloo, N2L3G1 Waterloo,sented by Ontario, Laing et Canada al.[5]. The modifications are needed to of the satellite[5].Quantum We keyproposeguaranteed distributionUniversityPatrick andUniversity by implement quantum J. (QKD)of Coles, Waterloo, of a theory. 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The researcherswhichfor cansomewhichfor to some beinvestigate unstructured can solved unstructured be solved effi the protocolsciently e securityffi protocolsciently with for withof which for significantly “unstructured” which significantly the key the ratekey fewer fewerBob’s rate was protocols, parameters was previouslyparameters state previously analyzer, i.e., unknown. than than those unknown. which the the that primal is primal beneficial lack problem, symmetry. problem, for andreceivers and that are of the fiber or the use of active opticsContents techniques to com- I. INTRODUCTION fibers are rotated by 90 relative to one another since type-2 • gives reliablegives reliable lower lower bounds bounds on the on the key key rate. rate. We WeIn illustrate illustrate the protocol, our our method method both by theby giving giving diagonal tight tight andlower lower the bounds boundscomputational Challenge for QKD implementations Our approach relies on transforming the key rate calculationlimited such tothe as as dual Quantum optimization Encryption problem, Science Satellite [10] R. Tannous,. MsC thesis, 2018. pensate for polarization somefor unstructured some fluctuations. unstructured protocols Polarization protocols for forwhich maintaining which the thebasis key key rate are rate observed was was previously previously to estimate unknown. unknown. the QBER on the channel, as spontaneous parametric down-conversion is used thus the en- which can be solved efficiently with significantly feweror parameters a mobile device. than the The primal omission problem, of the third and basis in Bob Arxiv 1905.09197 • How to align the reference frames fibers (PMF)I. are Introduction developedContentsContentsContents to specifically combat these rota- 1 • I.NewI. INTRODUCTIONI. INTRODUCTION INTRODUCTIONvariant of the protocol:tangled 6 – photons4 state are anti-correlated protocol in polarization, thus rota- gives reliable lower bounds on the key rate. We illustraterequiredrequires our for methodextracting adjusting by the a giving secure parameters tight key. lower used The in bounds QBER* the 6-stateDiag protocolis an tions [9]. However, these are only useful for applications thateffective QBER whichA. monitorsLaing et. al, any Phys. drop Rev. inA, 82(1):012304, the C-value. Jul For 2010. tion is necessary to ensure the photons Alice and Bob measure (e.g. polarization states at Alice have for some unstructured protocols for which the key ratepresented was previously in Laing unknown. et. al. [5].Z Z =(1 2Q) areI. limited IntroductionII. to the Results useContents of twoContents orthogonal polarizations, because1 2 I.I. INTRODUCTION INTRODUCTIONh ⌦ i experience similar walk-offs. The resulting entangled qubit I. IntroductionI. Introduction a1 more1 in-depthWe therefore analysis define of a the parameter QBER for RFI protocols, we to match Bob’s)? any polarizationA. not Setup aligned of tothe either problem of the two axes (slow and 2 Channel Verification: state (ignoring the vacuum component) at the output of the refer the reader to YoonZ et al.[11].Z =(1 From=(12Q the)2Q estimated) QBER II.fast) ResultsII.I. of Introductionthe Results fiberB. willContents Main be subject result to a rotational phase. We show2 12 3 (3,2)$protocol$I.h INTRODUCTIONh⌦ZZ⌦i ZiZ =(1 2Q) PMF’s can be approximated to, • Particular problem in our case is the II.I. Introduction Results an12 asymptotic key rate is estimatedh ⌦ 2 via[12],i 2 4 States (H, V, D, A) thatA. using SetupA. RFI SetupofC. protocols, the Generalof theproblem oneproblem framework can still use PMF’s for quantum 2 2 4 C =(3,2)$protocol$is$RFI!$XXAXBX+ =(1YAXB 2, Q) cos ✓ (1) A. Setup of the problem 2 Zhh Z⌦ i=(1i h 2Qi) · motion of the telescope II.B. ResultsMainB. Main result result 3 2 3 Key$rate$calculaBon$ h qZ⌦ iZ =(1 2Q) I.II. Introduction ResultsB. Main result1 2 3 Xh =(1X⌦ =(1i2Q)2Qcos) ✓cos ✓ 1 C.A. GeneralC.III. Setup General Discussion framework of frameworkthe problem 4 2 4 R 4 Q (Reference$frame$independence$1 fHX h (QBERX⌦ i )=(1H (QBER*2Q· ) cos ✓)) (4) if • Realtime Compensation: A. Setup of the problem 2 l h ⌦2 X i XHV 2 · Diag Y = ( 0 A 1 B + e 1 A 0 B) (5) C. GeneralB. Main frameworkA. result Reproducing literature results 4 3 4Constraints$$ hZ ⌦Z i=(1 =2(1Q) 2·Q) sin ✓ | i p2 | i | i | i | i II. Results 2 hX ⌦hXY ⌦i=(1X i 2Q) cos ✓ · III.B.III. Main DiscussionC. Discussion result GeneralB. Investigating framework unstructured protocols4where 3 44 Q 6 is the basish reconciliation⌦ i factor, · (1/6 in our case), l X X =(1 2Q) cos ✓ Location B 2 A. SetupA. of Reproducing the problemn literature results 2 4 Y X = (1 2Q) sin ✓ III.C. Discussion GeneralA. Reproducing framework1. MUBs literature resultsand 44 4 f is 6 the bidirectionY hh X⌦ error⌦= i correctioni(1 2Q) sin efficiency[13,·✓· 14], Location A e.g. Waterloo III. Discussion 4 h ⌦Y i X = (1 · 2Q) sin ✓ with f being the phase accumulated from the relative phase B. MainB. result InvestigatingB. Investigating2. Arbitrary unstructured unstructured angle protocols between protocols bases 3 6f = 6 1 in 7 our case assume error correctionWe$can$combine$these$two$constraints$ at the Shannon A. Reproducing literature results2 4 The security h of our⌦ current=(1=i V (1 internet2XQ2Q)=(1)cossin rests✓·✓2Q nervously) on e.g. Calgary A.1. n ReproducingMUBs literature results 6 4 X Y XX h ⌦ to$calculate$the$true$error$rate$i betweenwhere theM slowis and the fast expectationBob axis of the value PMF’s, of Alice the two and qubitBob’s positive- converted photons are then collected into PMF’s with the hor- III.C. DiscussionGeneralB. Investigating framework1. n MUBs3. unstructured B92 protocol protocols 4 limit.4 6 6 Itthe 7The is assumption important securityh h ⌦ to of⌦ note theouri i computational thatcurrent the analyticalinternet· · difficulty rests key of rate nervously certain of on h i B. Investigating unstructured protocols 6 = (1 2Q) sin ✓ opticaloperator elements valued6 andstats the measure– H, phaseV, D, A, of (POVM)L, R the pumpM laser., defined as, izontal and vertical polarizations aligned to the two principle A. Reproducing2. Arbitrary2.C. Arbitrary Conclusions literature angle angle between results between bases bases 7Eq. 4 7 4 doesproblems, 8TheAssumpBon:$The$dri,$is$slow$in$comparison$to$the$Bme$it$ not security account e.g., ofY for factoring. our any currentX mismatch=(1 For internet2 example,Q in) detection rests a nervously present-day efficien- on where M is the expectation value of the two qubit positive- converted1. photonsn MUBs are then collected into PMF’s with the hor- 6 thetakes$to$collect$data.$Hence$we$can$think$of$the$dri,$angle$ assumptionh V of⌦ theX i computational · difficulty of certain h i III. Discussion3. B921.3.n B92 protocolMUBs protocol4 7cies 6 7 northeeavesdropper the assumption vacuum orh can of multi⌦ recordthe photoncomputationali publicly contributions. announced difficulty We cipher-texts of take certain a After traversing through the PMF the signal is measured by axes, (slow and fast axis), of the PMF. Thus, the horizontal operator valued measure (POVM) M, defined as, izontalB. and Investigating2. Arbitraryvertical polarizations unstructuredangle between aligned protocols bases to the two principle 6 7 problems,The(theta)$being$constant$within$a$block$of$data.$ security e.g., of factoring. our current= (cos For✓ internet) example,(sin rests✓) a nervously present-day on C. ConclusionsIV.2. Arbitrary Methods angle between bases 8 7 problems,corresponding8 e.g.,Y to factoring. governmentX =V (1 For secrets.2 example,QX) Thensin ✓ a when present-dayY compu- M++ M+ M + + M A. ReproducingnC. Conclusions literature results 4 more 8 ineavesdropper depth lookh at this⌦can key-rate recordi publicly estimation announced· using numerical cipher-textsBob using a free-spaceM = 4-sate polarization analyzer while . the (2) and vertical polarizations are preserved while any other po- arxiv.org axes, (slow1.3. B92 andMUBs3. fastprotocol B92 axis), protocol of the PMF. Thus, the horizontal 6 7 7 theeavesdroppertational assumption tools can become of record the more computational publicly advanced announced in di theffi cipher-textsculty future, of e.g., certain M++ M+ M + + M methods later inThe Sec. security . of our current internet rests nervouslyidler on is measuredh by Alicei using a free-spaceÂijMij 6-state polariza- larization incident on the fiber will have a random rotational 2 1810.04112 M = . (2) andB. Investigatingvertical2. Arbitrary polarizations unstructured angle are between preserved protocols bases while any other 6 po- 7 Theproblems,correspondingcorrespondingifsecurity quantum e.g., ofV computers to= our to factoring. government(cos government current✓) areX internet built, secrets.(sin For secrets.✓) example, theY Then rests eavesdropper Then when nervously a when present-daycompu- can compu- on IV.C.IV. Conclusions MethodsC. MethodsV. Conclusions Acknowledgements 8 8 88 10 C will be constant even under varying phase theta, and if C drops <1, would reveal Eve! h i ÂijMij Airbornelarization Transmitter,1. n MUBs incident Smith on the Falls, fiber 2016 will have a random rotational 6 theeavesdroppertational assumptiontationaldecryptthe tools tools these assumption of can become becomesecrets. the record computational more of Suchmore the publicly advanced computational retroactive advanced announced di inffi theculty attacks in di future, theffi ofculty cipher-texts future,suggest certain e.g., of certain e.g.,tion analyzer. All single photon and coincidence counts are phase due to the difference in index of refraction between the Tomography Compensation 3. B92 protocol 7 problems, e.g., factoring. For example, a present-dayMij (i, j =+, ) are the coincidence counts of the various phase due to the difference in index of refraction between the problems,correspondingTheififthe quantum quantum security need e.g., for of computers factoring.immediatecomputers ourto government current are implementation areFor internet built, built, example,secrets. the rests the eavesdroppernervouslyThen ofa eavesdropper a morepresent-day when onrobust can compu- canmeasured and recorded using silicon avalanche photo-diodes, IV.C.2. MethodsV.IV. ArbitraryConclusions AcknowledgementsV. Methods AcknowledgementsReferences angle between bases 7 10 88810 10 eavesdropper can record publicly announced cipher-textswhere M is the expectation value of the two qubit positive- convertedslow and fast photons axis. The arethen axes alsocollected differ into in group PMF’s velocity with andthe hor- Mij (i, j =+, ) are the coincidence counts of the various thedecryptdecrypt assumptionmethod these thesefor secureof secrets. the secrets.EXPERIMENT computationalcommunication. Such Such retroactive retroactive difficulty attacks of attacks certain suggest suggesttenresults in total, for and the a time POVM taggingM and unit.Âij TheMij coincidencesis the total coincidenceare slow3. and B92 fast protocol axis. The axes also differ in group velocity 7 and eavesdroppertationalcorresponding tools can become record to publicly more government advanced announced secrets. in theThen cipher-texts future, when compu- e.g., h i thus the slow and fast component fo the polarization will be results for the POVM M and ÂijMij is the total coincidence problems,thetheOne need need e.g., candidate for for immediate factoring. immediate is quantum implementation For implementation example, key distribution a of present-day a of more a more(QKD), robust robustoperatormeasuredcounts valued using measured measure a 1 ns correlationsof M (POVM). By Pauli windowM, algebra, defined and accumulated we as, see that C 1, izontal and vertical polarizations aligned to the two principle 39 thusC. Conclusions theV. slowReferences AcknowledgementsReferences andA. fastTightness component forprotocols fo the polarization with MUBs will 8 10 be 10corresponding10eavesdropperif quantum1141tational can to computers government record tools become publicly are secrets. more announcedbuilt, advanced Then the cipher-texts eavesdropper when in the compu- future, can e.g., counts measured of M. By Pauli algebra, we see that C 1, IV.V. Methods Acknowledgements 810Themethod entangledmethodwhich generates for photons secure secure a communication. used keycommunication. betweenin the experiment two parties are (Alice created and over a 1 s integration time. Care was taken to ensure that the  temporally displaced after traversing the PMF. We call this  temporally displaced1. afterA general traversing lemma the PMF. We call this tationalcorrespondingdecryptBob) 11 tools whoseif these quantum become tosecrecy government secrets. computers more is guaranteed Such secrets. advanced are retroactive Then built, by in quantum when the the attacks future, compu-eavesdropper physics. suggeste.g., canwith the equality occurring for maximally entangled states. axes, (slow and fast axis), of the PMF. Thus, the horizontal with the equality occurring for maximally entangled states. using a SagnacOneOne candidate inteferometer is is quantum quantum[15] that key bidirectionally key distribution distribution pumps (QKD), (QKD),optical path efficiencyM++ of the bothM+ stateM analyzers+ + M are similar. displacement the walk-off. displacementA. TightnessA.References Tightness the walk-off.2. for Specific forprotocols protocols protocols with with MUBs MUBs 11 10if11tational quantumthewhichOriginally 12 need toolsdecrypt generates forcomputers become proposed immediate these a more keybysecrets. are betweenWiesner advanced implementation built, Such two[1], the in retroactive QKD theparties eavesdropper future,has of (Alice a developed attacks more e.g., and can robust suggestTherefore,M the= C-parameter effectively provides . a second(2) ba- and vertical polarizations are preserved while any other po- Therefore, the C-parameter effectively provides a second ba-IV.V. Methods AcknowledgementsReferences 8 a1010 type-2which periodically generates poled a potassium-titanylkey between two phosphate parties with(Alice andHowever, the detection efficiencies may vary between all the 1. A1. general A generala. lemma Two lemma MUBs 11 decrypt 11ifmethod quantumBob)dramatically 12 these whosethe for computers need secrets. secure secrecy over for the immediatecommunication. areis Such pastguaranteed built, retroactive three implementation the decadesby eavesdropper quantum attacks [2, 3], of physics. aboth can suggest more in robustsis thath cani be useful in a quantumijMij communication context, larizationThe entangled incident photons on the travel fiber through will have 2 m a of random 780 nm rotational PM sis that can be useful in a quantum communication context, The entangled photons travel through 2 m of 780 nm PMthe signalBob) at whose776method nm secrecy and forsecure theis idler guaranteedcommunication. at 840 nm. by Details quantum of the physics.detectors and should be noted as this is a crucial part of our A.2. TightnessSpecific2. Specific protocolsb.for protocols Six-state protocols protocol with MUBs 12 11the 12decrypt needOriginallytheoryOne 13 forthese candidate and immediate proposed secrets. implementation. is Suchby implementation quantum Wiesner retroactive Indeed, [1], key QKD QKDattacks distribution of hasa is more nowsuggest developed a robust com- (QKD), fibers and which are rotated by 90 relative to one another. and will be called the "diagonal*" basis. The C value is used V.fibersA. Acknowledgements Tightness and which forare rotated protocols by 90 with relative MUBs to one another.10 entire11 the experimentalOriginally needmercial for technology,One immediate proposed setup candidate can withimplementation by be isthe Wiesner found quantum prospect in [1], ofFig keyof a QKDglobal 1.more distribution The robusthas QKD down developed net- (QKD),securityand willbelow. be called the "diagonal*" basis. The C value is used phase due to the difference in index of refraction between the Referencesa.1. Two Aa. general Two MUBsc. MUBsn lemmaMUBs 1210 11method 12 whichdramatically 13 for generates secure over communication. a the key past between three decades two parties [2, 3], both (Alice inM and(i, j =+, ) are the coincidence counts of the various to monitor the quality of the quantum channel and any signif- The equality of the lengths of the fibers is critical since the methodworks forwhich on secure the generates horizon communication. [4, a 5]. key between two parties (Aliceij andto monitor the quality of the quantum channel and any signif- The equality of the lengths of the fibers is critical since the 1. A generalb.2. Six-state Specificb. Six-state lemma protocols protocol protocol 13 11 12 13OneBob)dramaticallytheory candidate whose and implementation. secrecy over is quantum the is pastguaranteed Indeed, key three distribution QKD decades by quantum is now [2,(QKD), a 3], com- physics. both in slow and fast axis. The axes also differ in group velocity and icant drop from unity can be attributed to an eavesdropper’s walk-offReferences induced to Alice’s photons should be the same10 for OnemercialThe candidateBob) maintechnology, whose theoretical is quantum withsecrecythe problem iskey prospect guaranteed distribution in QKD of global by is (QKD),toquantum QKD calculate net- physics.results for the POVM M and ÂijMij is the total coincidence walk-off induced to Alice’s photons should be the same for A. Tightness2. Specificc. nB.a.c.MUBsfor protocols Two Arbitraryn MUBs protocols MUBs post-selection with MUBs 1311 12 12which 13 Originallytheory14 generates and proposed implementation. a key bybetween Wiesner Indeed, two [1], parties QKD QKD has(Alice is now developed and a com- icant drop from unity can be attributed to an eavesdropper’s thus the slow and fast component fo the polarization will be Bob’s photon. The walk-off must be less than the pump’s co- whichworkshow generates much onOriginally the secret horizona key proposed key between [4, can 5]. be by twodistributed Wiesner parties [1], by (Alice QKD a given hasand pro- developed intervention[5]. C is a statistical value and it can be shown to a. Twob. MUBs Six-state protocol 12 13Bob)dramaticallymercial whose technology, secrecy over is the guaranteedwith past the three prospect by decades quantum of global [2, physics.3], QKD bothcounts net- in intervention[5]. measured of MC.is By a statistical Pauli algebra, value and we it see can that be shownC 1, to Bob’s photon. The walk-off must be less than the pump’s co- 1. A general lemma 11 Bob)tocol.The whosedramatically mainThis secrecy is theoretical the iskeyguaranteed over rate problem the problem past by in three, quantumQKD where decades is key to physics. rate calculate [2, refers 3], both in  temporally displaced after traversing the PMF. We call this be constant even in the presence of a relative phase between A.herence Tightness time,B. Arbitraryfor sinceC. protocolsn Strong the coherence post-selection duality with time MUBs of the entangled11 pho- Originally14 works14 on proposed the horizon by Wiesner [4, 5]. [1], QKD has developedwith the equality occurring for maximally entangled states. 2.B. Specificb. Arbitrary Six-statec. protocolsMUBs post-selection protocol14 12 13 13Originallytheoryhowto the much andtheory proposed number secret implementation. and of by key implementation. bits Wiesner can of be secret [1],distributed Indeed, QKD key Indeed, established has QKD by developed QKD agiven is now isdivided now pro- a com- a com-be constant even in the presence of a relative phase between herence time, since the coherence time of the entangled pho- the X and Y bases (for both qubits) for a phase that can be tons is transfered from the pump [16, 17]. For our experiment dramaticallyThe main over theoretical the past three problem decades in QKD [2, 3], isto both calculate in displacement the walk-off. 1. A generalc. n MUBs lemma 11 13 dramaticallymercialtocol.by the Thismercial technology, number over is the technology, the ofkey past distributed with rate threethe problemwith decadesprospectthe quantum,prospect where [2, of systems. key3], global of both rate globalQKD refersin Even QKDTherefore, net- net-the X theandCY-parameterbases (for effectively both qubits) provides for a phase a second that can ba- be tons is transfered from the pump [16, 17]. For our experiment approximated as being constant over the finite measurement the fibersa. induce Two MUBs a walk-off of approximately 2.34 ps and the 12 how much secret key can be distributed by a given pro- 2. SpecificC.B. StrongC. Arbitrary Strong protocolsD. duality Arbitrary duality post-selection key-map POVMs 1214 14theory14theoryworkstoif16 Aliceandthe and onworks number implementation. implementation. and theon Bobhorizon of the bitshave horizon[4, of fully Indeed, secret 5]. Indeed, [4, characterized 5]. key QKD QKD established is now is their now a com- divided devices, a com- R. Tannous, APPLIED PHYSICS LETTERS, 115(21), 2019. The entangled photons travel through 2 m. of 780 nm PM coherenceb. time Six-state of the protocol 405 0.005 nm pump is approximately 13 tocol. This is the key rate problem, where key ratesis refers thatapproximated can be useful as being in a quantum constant over communication the finite measurement context, the fibers induce a walk-off of approximately 2 34 ps and the interval. For additional comments on the security also see a. Two MUBs 12 mercialmercialbytheyThe thetechnology, technology, still main number may theoretical not withof withdistributed know the theprospect their problem prospect key quantum of rate in globalof QKD globalsince systems. QKD the is QKD tonet- optimal Even calculate net- B. Arbitraryn post-selection± 14 and willinterval. be called For the additional "diagonal*" comments basis. on The theC securityvalue is also used see fiberscoherence and time which of the are 405 rotated0.005 by nm 90 pumprelative is approximately to one another. Laing et al. [5]. 1.08 ns.D.c. IfC.ArbitraryD. the Strong ArbitraryMUBs difference dualitykey-map key-map in thePOVMs walk-off POVMs is too large, the pho-16 1314works16workshowtoifeavesdroppingonAlice the on much the the number and horizon secret Bob attack of have key[4, [4, bits 5]. for 5].can fully oftheir be secret characterized protocol distributed key may established their beby unknown. a devices, given divided pro- ± b. Six-state protocol 13 1.08 ns. If the difference in the walk-off is too large, the pho- The channel integrity is monitored by observing the corre- tons become distinguishable and the quality of entanglement Thetocol.bythey mainthe still This numbertheoretical may is the not ofkey know distributed problem rate their problem key in quantumrate QKD, where since is theto systems. key calculate optimal rate refersto Even monitorLaing the et al. quality [5]. of the quantum channel and any signif- The equality of the lengths of the fibers is critical since the Experimental Setup C.c. Strongn MUBs duality 13 14 Results 4 lation in both computational and "diagonal" basis. The quan- isB. reduced. ArbitraryD. The Arbitrary coherence post-selection key-map of the pumpSlow POVMs wasaxis closely= V monitored1416howtoifeavesdropping much Alicethe number secret and Bob attackkey of bitscanhave for be of their fully distributedsecret protocol characterized key may established by be a unknown.given their dividedpro- devices,icant dropThe from channel unity integrity can be is attributed monitored toby an observing eavesdropper’s the corre- walk-offtons become induced distinguishable to Alice’s and photons the quality should of entanglement be the same for tum bit error ratios (QBER) in the computational basis and the with a spectrometer, as see in Fig 1. The pump laser was tocol.bythey Thisthe still number is may the key not of ratedistributed know problem their key, quantum where rate key since systems. rate the refers optimal Even lation in both computational and "diagonal" basis. The quan- is reduced. The coherence of the pump was closely monitored B. Arbitrary post-selection 14 intervention[5]. C is a statistical value and it can be shown to Bob’s photon. The walk-off must be less than the pump’s co- "diagonal" basis are given by, somewhatC.D. Strong Arbitrary unstable duality key-map such thatPOVMs it would frequently jump from1416to theifeavesdropping Alice number and of Bob attackbits have of for secret fully their characterized key protocol established may their be divided unknown. devices,Thetum phase bit error is varied ratios by (QBER) tuning a in birefringent the computational element. basis and the with a spectrometer, as see in Fig 1. The pump laser was by the number of distributed quantum systems. Evenbe constant even in the presence of a relative phase between herence time, since the coherence time of the entangled pho- 1 Z Z Nbad single frequency mode operation to multi-frequency mode op- they still may not know their key rate since the optimal • Transmission QBERoverHV = h ⌦ i = , "diagonal" basis are given by, somewhat unstable such that it would frequently jump from 2 Ntotal C.eration. Strong It duality was observed that this also reduced the quality14 of if Alice and Bob have fully characterized their devices,the X and Y bases (for both qubits) for a phase that can be tons is transfered from the pump [16, 17]. For our experiment D. Arbitrary key-map POVMs Fast axis = H 16 eavesdropping attack for their protocol may be unknown. single frequency mode operation to multi-frequency mode op- polarization maintainingQBER* = fiber1 C . (3) the entangled source and thus the pump spectra needed to be they still may not know their key rate since the optimalapproximatedCoincidence as being Counts constant1 overZ Z the finiteNbad measurement the fibers induce a walk-off of approximately 2.34 ps and the Diag 2 QBERHV = h2⌦ i = N , D.monitored Arbitrary in orderkey-map to perform POVMs our protocol with PMF’s.16 The eavesdropping attack for their protocol may be unknown. total eration. It was observed that this also reduced the quality of interval. For additional comments on1 theC security also see coherence time of the 405 0.005 nm pump is approximately 3 QBER* = . (3) the entangled source and thus± the pump spectra needed to be In the protocol, both the diagonal and the computational fibers are rotated by 90 relative to one another since type-2 Laing et al. [5]. Diag 2 1.08 ns. If the difference in the walk-off is too large, the pho- basis are observed to estimate the QBER on the channel, as spontaneous parametric down-conversion is used thus the en- monitored in order to perform our protocol with PMF’s. The tangled photons are anti-correlated in polarization, thus rota- The channel integrity is monitored by observing the corre- tons become distinguishable and the quality of entanglement required for extracting a secure key. The QBER*Diag is an In the protocol, both the diagonal and the computational fibers are rotated by 90 relative to one another since type-2 lation in both computational and "diagonal" basis. The quan- is reduced. The coherence of the pump was closely monitored effective QBER which monitors any drop in the C-value. For tion is necessary to ensure the photons Alice and Bob measure basis areTomography observed to to determine estimatethe purity QBER of state on the channel, as spontaneous parametric down-conversion is used thus the en- experience similar walk-offs. The resulting entangled qubit tum bit error ratios (QBER) in the computational basis and the with a spectrometer, as see in Fig 1. The pump laser was a more in-depth analysis of the QBER for RFI protocols, we Birefringent walkoff required for extracting a secure key. The QBER* is an tangled photons are anti-correlated in polarization, thus rota- refer the reader to Yoon et al.[11]. From the estimated QBER state (ignoring the vacuum component) at the output of the Diag somewhat unstable such that it would frequently jump from "diagonal"effective basis QBER are given which by, monitors any drop in the C-value. For tion is necessary to ensure the photons Alice and Bob measure an asymptotic key rate is estimated via[12], PMF’s can be approximated to, single frequency mode operation to multi-frequency mode op- a more in-depth analysis1 of theZ Z QBERNbad for RFI protocols, we experience similar walk-offs. The resulting entangled qubit QBERHV = h2⌦ i = N , refer the reader to Yoon et al.[11]. Fromtotal the estimated QBER eration.state (ignoring It was the observed vacuum that component) this also at reduced the output the of quality the of 1 1 C ( ( ) ( )) if QBER* = . (3) thePMF’s entangled can be approximated source and thus to, the pump spectra needed to be R Ql 1 fH2 QBERHV H2 QBER*Diag (4) Y = ( 0 A 1 B + e 1 A 0 B) (5) an asymptotic key rate isDiag estimated2 via[12], | i p2 | i | i | i | i monitored in order to perform our protocol with PMF’s. The where Q is the basis reconciliation factor, (1/6 in our case), l In the protocol, both the diagonal and the computational fibers are rotated by 90 relative to one another since type-2 and f is the bidirection error correction efficiency[13, 14], 1 if with f being the phase accumulated from the relative phase R Ql (1 fH2(QBERHV ) H2(QBER*Diag)) (4) spontaneousY parametric= ( 0 down-conversion1 + e 1 0 is used) thus(5) the en- f = 1 in our case assume error correction at the Shannon basis are observed to estimate the QBER on the channel, as | i p | iA | iB | iA | iB between the slow and fast axis of the PMF’s, Alice and Bob’s tangled photons are2 anti-correlated in polarization, thus rota- limit. It is important to note that the analytical key rate ofR. Tannous, APPLIED PHYSICS LETTERS, 115(21), 2019. required for extracting a secure key. The QBER*Diag is an optical elements and the phase of the pump laser. where Ql is the basis reconciliation factor, (1/6 in our case), FIG. 1:Eq. Experimental 4 does setup, not a 405 account nm laser is for used anyto pump mismatch a type-2 periodically in detection poled potassium-titanyl efficien- phosphate (PPKTP) effective QBER which monitors any drop in the C-value. For tion is necessary to ensure the photons Alice and Bob measure in a Sagnaccies interferometer[15].nor the vacuum Entangled or 776 multi nm and photon 840 nm photons contributions. are collected into 780 We nm polarization take a maintainingAfter traversing through the PMF the(a) Systemsignal left is undisturbed.Top: measured by the experimental expectation (b) Varying phase induced by a HWP in Alice’s analyzer. Top: and f is the bidirection error correction efficiency[13, 14], fibers that induce a relative phase that causes rotations in the X and Y bases. Alice performs a complete, six-state measurement values and phase f. The average C value is C = 0.97(1) . the experimental expectation values and phase f. The average experiencewith f being similar the phase walk-offs. accumulated The from resulting the relative entangled phase qubit on the 840 nm photon, while Bob performs a tomographically incomplete four-state measurement on the 776 nm photon. Ten a more in-depth analysis of the QBER for RFI protocols, we more in depth look at this key-rate estimation using numerical Bob using a free-space 4-sate polarizationMiddle: analyzerPurity and concurrence while the of the entangled state after the C value is C = 0.96(4). Middle: Purity and concurrence of the f = 1 in our case assume error correction at the Shannon 42 silicon avalanche photo diodes are used to detect the photons, coincidence and single events are recorded and analyzed by a 43 statebetween (ignoring the slow the and vacuum fast axis component) of the PMF’s, at Alice the and output Bob’s of the time-taggingmethods unit andlater a computer. in TheSec. spectrometer . is used to monitor the pump spectra as a single frequency mode isidler critical is measured by Alice using a free-spacetransmission 6-state through polariza- the PM fibers. Bottom: QBER and key entangled state after the transmission through the PM fibers.refer thelimit. reader It is to important Yoon et al.[11].to note that From the the analytical estimated key QBER rate of rate. The average QBER is 0.0112(4) and total QBER is Bottom: QBER and key rate during the phase change. The for a successful key transfer. * indicates the half-wave plate rotated about its vertical axis which is used to manipulate the ⇤Diag PMF’soptical canelements be approximated and the phase to, of the pump laser. external the phase allowing for phase variations to be very rapid. tion analyzer. All single photon and0. coincidence021(6). The average counts estimated are key is 0.139(6). The key rate average QBER Diag is 0.022(2) and total QBER is 0.03an(1). asymptoticEq. 4 does key not rate account is estimated for any mismatch via[12], in detection efficien- ⇤ measured and recorded using silicon avalancheis the normalized photo-diodes, key rate (per coincidence) from Eq. 4. The average estimated key rate is 0.13(1). The key rate is the cies nor the vacuum or multi photon contributions. We take a After traversing through the PMF the signal is measured by EXPERIMENT normalized key rate (per coincidence) from Eq. 4. RESULTS AND DISCUSSIONS QBER and key rate estimates ten in total, and a time tagging unit. The coincidences are more in depth look at this key-rate estimation using numerical Bob using a free-space 4-sate polarization analyzer while the measured using a 1 ns correlationsFIG. window 2: Experimental and accumulated results, the shaded regions represent the calculated error in the respective value. Error bounds are present 1 if From the correlation data, the QBER is estimated according ( ( ) ( )) methodsR Ql later1 infH Sec.2 QBER . HV H2 QBER*Diag (4) idler is measuredY = by Alice( 0 usingA 1 aB free-space+ e 1 6-stateA 0 B) polariza- (5) We presentThe the results entangled of two experimental photons conditions. used The in theto Eq. experiment 3. Note that even with are the created presence of a randomover rela- a 1 s integration time. Care wasintaken the top andto ensure bottom figures, that the however, some might be too small to be visible. The error bounds are derived using error | i p | i | i | i | i first case (trial (a)) is where the system was left undisturbed tive phase induced by the fiber and the birefringent element, propagation of the statistical counting error. No error analysis is provided for the tomographically derived values (purity, tion analyzer. All single2 photon and coincidence counts are such thatusing the rotational a Sagnac phase is only inteferometer due to the difference [15] in a that low overall bidirectionally QBER is maintained. pumps We calculated theoptical aver- path efficiency of the both stateconcurrence). analyzers The key are rates similar. in this figure are calculated using the raw coincidence data to compute the various expectation . ( ) . ( ) where Ql is the basis reconciliation factor, (1/6 in our case), the indicesa type-2 of refraction periodically between the slow and poled the fast potassium-titanylaxis of age total QBER ofphosphate 0 021 6 for trial (a)with and 0 03 1 However,for trial the detection efficienciesvalues, may Eq. vary 2, which between is then all used the to compute the QBER, Eq. 3, which is then used in Eq. 4 to get the key rates shown above. measured and recorded using silicon avalanche photo-diodes, the PMF’s. In this configuration, any phase changes can be (b). For systems based on qubits, a total QBER of less than and f is the bidirection errorEXPERIMENT correction efficiency[13, 14], 5 attributedthe to stress signal of the fiber, at 776 whether nm it be and thermal the or physi- idler0 at.11 is 840 required, nm. thus Details our observed of QBER the results aredetectors below and should be noted as this is a crucial part of our withten inf total,being and the a phase time tagging accumulated unit. The from coincidences the relative are phase cally induced.entire The experimental second case (trial (b)) issetup where an can external be foundthe threshold in of Fig 0.11 required 1. The to perform down a secure keysecurity transfer below. f = 1 in our case assume error correction at the Shannon birefringent element is used to increase changes in the phase and therefore, indicates that this protocol is robust to phase the security of the protocol, we take a closer look at the key events. Usually, a rigorous finite size security analysis would measured using a 1 ns correlations window and accumulated allowing for phase variations to be very rapid as needed. [18] drifts despite the lack of complete measurements. between the slow and fast axis of the PMF’s, Alice and Bob’s rate by taking into account the effects of the different detection work with frequencies, but this is beyond the scopelimit. of the ItThe is important entangled photons to note used that in the the analytical experiment key are rate created of over a 1 s integration time. Care was taken to ensure that the Both experimental trials were done in a controlled laboratory Given the low overall QBER, an asymptotic normalized key optical elements and the phase of the pump laser. setting and measurements were taken for 2-3 minutes. rate (per coincidence) is estimated for both trials using Eq. 4, efficiencies in the various detection paths on both Alice’s and current analysis. Instead, we utilize a maximumEq. likelihood 4 doesusing not a Sagnac account inteferometer for any mismatch [15] that in bidirectionally detection efficien- pumps optical path efficiency of the both state analyzers are similar. the results are shown in Fig. 2. The drop in key rate in trial (b) Bob’s side. In this scenario we cannot make a fair sampling approach to convert frequencies to probabilities. In the third From the measurements we compute the expectation values is correlated to the spike in QBER that is exhibited during a assumption. We implement a detailed modeling of the phys- step, using the determined detection efficiencies andcies observa- nora type-2 the vacuum periodically or multi poled photon potassium-titanyl contributions. phosphate We take with a However,After traversing the detection through efficiencies the PMF may the vary signal between is measured all the by of all the possible POVM’s using Eq. 2 and calculate the C- rapid phase change, up to approximately 0.7 rad/s. The aver- ical set-up, and perform a numerical security analysis along tion probabilities derived from the quantum state estimation parameter. Indeed for trial (a), the C-parameter appears to be age key rate value for trial (a) is 0.139(6) and 0.13(1) for trial more inthe depth signal look at 776 at this nm andkey-rate the idler estimation at 840 nm. using Details numerical of the Bobdetectors using and a free-space should be noted 4-sate as polarization this is a crucial analyzer part of while our the constant as a function of the phase Fig. 2, as expected from the (b), while the theoretical limit of the key rate per coincidence the lines of Winick et al. [19]. procedure, we perform an asymptotic numerical security anal- definition of C. However, in Fig. 2 (b) we see some variation of our system, given by Eq. 4, is 0.167. ysis. methodsentire later experimental in Sec. . setup can be found in Fig 1. The down idlersecurity is measured below. by Alice using a free-space 6-state polariza- of C, which can be attributed to a rapid change in the relative The analytical estimated key rate given from Eq. 4 only pro- To accomplish this, we follow three steps. In the first step, phase. This drop in C-parameter is also correlated to a drop in vides an estimation for the final key rate as it does not account we analyze the data to find self-consistent values of the detec- In our calculations, we make the assumption that the sig- tion analyzer. All single photon and coincidence counts are the inferred state purity. for detection efficiency mismatches. Thus to further underline tion efficiencies for the various polarization detection paths. nals in each arm are restricted to vacuum and single photon In the second step, we deal with the fact that the experi- states in polarization. Also, to facilitate the second step, we measured and recorded using silicon avalanche photo-diodes, ments provides frequencies of observed events. However, impose a time interval structure onto our data to catch the ef- EXPERIMENT ten in total, and a time tagging unit. The coincidences are our asymptotic key rate calculation requires probabilities of fect of vacuum detections which is extremely predominant in measured using a 1 ns correlations window and accumulated The entangled photons used in the experiment are created over a 1 s integration time. Care was taken to ensure that the using a Sagnac inteferometer [15] that bidirectionally pumps optical path efficiency of the both state analyzers are similar. a type-2 periodically poled potassium-titanyl phosphate with However, the detection efficiencies may vary between all the the signal at 776 nm and the idler at 840 nm. Details of the detectors and should be noted as this is a crucial part of our entire experimental setup can be found in Fig 1. The down security below. JEONGWAN JIN et al. PHYSICAL REVIEW A 00,003800(2018)

careful alignment we were able to obtain only a maximum vis- 111 multi ibility of 0.16 0.01, which, as shown in Fig. 2(e), 112 V0 = ± drops to zero with an AOI of 0.2◦.Theseobservationsclearly 113 show that, given the expected angular deviations reported for 114 free-space quantum channels, it would be technically very 115 challenging to achieve a reliable, stable, and efficient operation 116 of time-bin qubit analyzers using standard interferometers. 117 the incident angles β1 on the primary mirror and β2 FIG. 1. Time-bin-based quantum communication in a turbulent on the second mirror can be expressed free-space channel. When a time-bin-encoded photon, whose path is These interference challenges are overcome by utilizing 118 β1 ≈ ρ∕ 2f 1 ; (26) relay optics in the long arm of the unbalanced Michelson 119 † deviated by atmospheric turbulence as well as telescopes misalign- interferometer (Method 1). The idea is to reverse differences 120 β2 ≈ ρ∕ 2f 1 ρ C · f 1 − f 2 ∕ 2f 1f 2 ; (27) Depolarization of a Laser Beam at 6328 A due to †‡‰ †Š † ment, enters a time-bin receiver with variable angle of incidence α,a Atmospheric Transmission in the evolution of spatial modes over the length #l in the 121 where C is the blocking ratio of the telescope. lateral offset δ(α)occursbetweenthepaths(redandblueline)atthe The corresponding rotation angles of Ω1 and Ω2 can D. H. Hhn 122 be deduced according to the method in [14] interferometer exit. This is due to the receiver length asymmetry and long arm, as shown in Fig. 2(c).Thiseffectivelyguarantees identical wavefront evolutions in the short and long paths of 123 The depolarization of a linearly polarized laser beam was investigated primarily with an optical path of 4.5 2 Ω1 0.5 arcsin A · sin αi B · sin 2αi ∕β ; (28) reduces the interference quality, resulting in lower distinguishability km. A He-Ne gas laser at 6328 A was used with an additional polarizer at the output and with a ro- ˆ †‡ †† 1 tating polarization filter assembly in front of the receiver. Values of depolarization found ranged between 124 10-7 rad and about 5 X 10- rad. The lower limit was determined by the quality of the polarizer-ana- of the time-bin states in superposition bases. Turbulence-induced the interferometer. Consequently, spatial indistinguishability lyzer combination used. These experimental values of depolarization are very much higher than that pre- dicted by theories regarding turbulence-induced depolarization. Fig. 2. Measurement error, induced by a Newton telescope with 0.5 arcsin A · sin α B · sin 2α ∕β2 : Ω2 i i 2 Ω1 125 an aluminum coating, changes with the parameter da, and it has a ˆ †‡ †† ‡ spatial-mode distortions further lower the interference visibility (see is restored regardless of spatial mode and AOI of the input range of 0–1; complex refractive index of the coating N is (29) I. Introduction Sec. II, the results of the measurements made near 0.877 6.479i. 126 Tilbingen should not be compared directly with any one ‡ A and B depend on the coordinate ρ, but they are text for details). beam. For verification, we set #l 0.60 m (2.0 ns) and The results of an experimental study of the depolar- theory, but should be discussed in light of the theoretical independent of α. The exact values of the coefficients ization of a linearly polarized laser beam traversing the situation at present. In the Tubingen experiments, a = atmosphere near ground level are presented and dis- 7/31/20 127 range of 4.5 km was usually used. The experiments The depolarization coefficient k induced by the A and B does not matter. measure interference visibilities by applying voltages to a piezo cussed in this paper. were conducted at night from the middle of 1966 until A theoretical prediction, probably the first one con- telescope is 0.946. According to Eqs. (6) and (25), A Cassegrain telescope with F number F 3 is the middle of 1967. Using a rotating-filter method ˆ cerned with turbulence-induced polarization fluctua- similar to that used by Saleh,4 depolarizations were the measurement error of depolarization parameter also chosen as our simulated model. Its detail param- 128 tions, was published by Hodara, but his results were in mounted on a mirror in the short path, allowing it to change the 2 found. The root-mean-square variation of the angle of d error by some orders of magnitude, even if actual polarization a,, used as a parameter for the depolariza- a induced by the telescope is illustrated in Fig. 2 for eters are shown in Table 2. measurements2 seemed to confirm his theory. Fried 79 II. MULTIMODE TIME-BIN ANALYZER METHODS 3 tion, is compared with the root-mean-square variation when the telescope polarization crosstalk is not con- The Mueller matrix of the Cassegrain telescope in phase of the interferometer at various AOIs. Having a single- 129 and Mevers found very high degrees of polarization of the logarithm of intensity slog ,, from which the struc- fluctuations experimentally but "now it seems that this ture constant of the index of refraction C. can be de- sidered. The error changes with the parameter da, Table 2 is rather large measured value was mainly due to a defect in duced; C. is a characteristic parameter of atmospheric the experiment." 4 Strohbehm and Clifford5 presented a 130 turbulence.6 80 mode beam as an input, we obtain an interference visibility new theory on turbulence-induced polarization fluctua- Let us consider an unbalanced Michelson interferometer tions. A first order solution to the wave equation was single 4 11. Theoretical Results found using spectral analysis techniques. Finally, Saleh 0 8517 3 694 10−3 00 of 0.91 0.01, which remains constant as the AOI 131 published a theory on polarization fluctuations using A. Polarization Fluctuations . − . · 81 with long and short paths of lengths lL and lS,respectively. Chernov's −3 −13 −14 the geometrical optics approximation and If the laser beam is polarized linearly at the trans- −3.694 · 10 0.8517 −7.15 · 10 −1.6 · 10 V = ± three-dimensional ray statistical model, together with M 0 1: mitter output, the root-mean-square variation a-,, of the C −15 −13 (30) is varied [see Fig. 2(d)]. The visibility and error are extracted 132 some experimental results. The sensitivity of his angle of polarization 0 induced by atmospheric turbu- ˆ −2 · 10 7.15 · 10 0.8513 0.0273 82 While the path-length difference for zero-angle incidence measurements was limited by the equipment used, to lence is given by B 000.0273 0.8513 C -42 dB in the daytime and -45 dB at night. No B − C from a sinusoidal fit of measured data. The improvement is 133 depolarization-corresponding to time- or space-aver- II: 1 Myth:(An2)'/2 l You can only useB polarization encoding C 83 aged fluctuations of the polarization angle of a linearly = - 1'/2 >,) (1) @ A is simply #l0 2(lL lS), a nonzero AOI translates into polarized laser beam-was found at a propagation The issue with asymmetric= MZI− and distorted range of 2.6 km. In agreement with his theory, it must if we follow the theory of Strohbehm and Clifford [Ref. 84 further confirmed by measurements with a multimode beam 134 be much smaller as long as turbulence is the only source 5, Eq. (9) ]. An is the deviation of the index of refrac- and a greater measurement error can be found when When it is used in polarization lidar, the depolari- an angle-dependent path length and a lateral offset as the tion of the atmospherein freefrom its mean, -normalizedspace to quantum communications of depolarization. the depolarization parameter d becomes smaller. zation parameter da of aerosol is multi Because of the fact that the above-mentioned theoret- unity; is the scale factor of the gaussian approxima- a modes [Fig. 2(b)]wherethehighvisibilityof 0.89 0.01 135 spectral density of the ical predictions are contradictory, which is shown in tion of the three-dimensional The maximum error can reach 5.7% when da is close 85 beam propagates. Using geometrical ray tracing through the index Depolarizationof refraction used, of and a Laser may beBeam considered at 6328 to be A due to to zero. V = ± the correlation length [Ref. 5, Eq. (31) ]; X is the wave- Polarization effect of mirrors due to Fresnel-coefficients 136 length;Atmospheric L is the range Transmission of propagation. Assuming An 2 2I⊥ 86 [Fig. 2(e)]demonstratesthattheinterferometerdesignisrobust The author is with the Astronomisches Institut der Universitdt d z . (31) • interferometer, we find that the path-length difference is given Tdbingen, Waldhauserstrasse 64, Ttibingen 74, Germany. = 10-12 and = 10 cm, corresponding to strong tur- B. Mueller Matrix of a Cassegrain Telescope a 1 0087I I Different incident angles and modal distortions experience different Received 6 August 1968. bulenceD. H.near Hhn the ground, we find when X = 632.8 nm †ˆ . ∥ ⊥ A Cassegrain telescope can be achieved by two mir- ‡ Phase 87 by against highly distorted beams. This is noteworthy as it allows 137 February 1969 / Vol. 8, No. 2 / APPLIED OPTICS 367 rors; a large concave paraboloidal primary with a The depolarization of a linearly polarized laser beam was investigated primarily with an optical path of 4.5 km. A He-Ne gas laser at 6328 A was used with an additional polarizer at the output and with a ro- The induced depolarization coefficient is 1.0087. JEONGWAN JIN et al. usPHYSICAL to couple REVIEW the output A 00,003800(2018) of the interferometer into a multimode 138 tating polarization filter assembly in front of the receiver.-7 Values of depolarizationcentral found ranged hole,between and a small hyperboloidal convex mir- Dpolarization10-7 measured ca. 10 to the polarizer-ana- rad and about 5 X 10- rad. The lower limit was determined by the quality of We also assume that the laser is aligned to the • Tim—bin analyzer interferometer with ‘flat’ optics not suitable -5 lyzer combination used. These experimental values of depolarization are veryror. much higher It than is that shown pre- in Fig. 3. 10 rad. dicted by theories regarding turbulence-induced depolarization. If its focal length of the primary mirror is denoted optical axis of telescope. Similarly to Fig. 2 in the #l0 1 1 tan(α) fiber, yielding a high coupling efficiency of 0.87 for delivery of 139 Limited by apparatus and by f , and the focal length of the second mirror is f , previous section, the measurement error induced 1 made near 2 #l α careful alignment we were able to obtain only a maximum vis- 111 Sec. II, the results of the measurements ( ) I. Introduction Breckinridge, Lam, Chipman, Publications of the Astronomical Society of the Pacific, Vol. 127, No. 951 (2015), pp. 445 − Tilbingen should not be compared directly with any one The results of an experimental study of the depolar- by the Cassegrain telescope is shown in Fig. 4. background light. theory, but should be discussed in light of the theoretical multi photons to the detector. Phase-recovery capacity is discussed 140 ization of a linearly polarized laser beam traversing the situation at present. In the Tubingen experiments, a The maximum measurement error is less than = 2 cos(α) + cos(α) sin(α) ibility of 0.16 0.01, which, as shown in Fig. 2(e), 112 atmosphere near ground level are presented and dis- range of 4.5 km was usually used. The experiments 0 cussed in this paper. were conducted at night from the middle of 1966 until ! " V = ± A theoretical prediction, probably the first one con- 1%, even if the polarization crosstalk is not + the middle of 1967. Using a rotating-filter method drops to zero with an AOI of 0.2 .Theseobservationsclearly 113 141 cerned with turbulence-induced polarization fluctua- 4 in the section◦ Measurements and Results. similar to that used by Saleh, depolarizations were tions, was published by Hodara, but his results were in considered. π found. The root-mean-square variation of the angle of error by some orders of magnitude,2 even if actual 2 polarization a,, used as a parameter for the depolariza- show that, given the expected angular deviations reported for 114 measurements seemed to confirm his theory. Fried tion, is compared with the root-mean-square variation and Mevers3 found very high degrees of polarization δ(α)tan α , (1) of the logarithm of intensity slog ,, from which the struc- The second type of interferometer we study is based on the 142 fluctuations experimentally but "now it seems that this ture constant of the index of refraction C. can be de- 115 rather large measured value was mainly due to a defect in duced; C. is a characteristic parameter of atmospheric free-space quantum channels, it would be technically very the experiment." 4 Strohbehm and Clifford5 presented a + − 4 turbulence.6 Table 2. Parameters of the Cassegrain Telescope new theory on turbulence-induced polarization fluctua- 143 tions. A first order solution to the wave equation was 11. Theoretical Results challenging to achieveuse a reliable, of media stable, with and different efficient operation refractive116 indices for the paths of the found using spectral Whatanalysis techniques. about Finally, Time Saleh4 - # $ published a theory on polarization fluctuations using A. Polarization Fluctuations Entrance pupil diameter D 667 mm the geometrical optics approximation and Chernov's If the laser beam is polarized linearly at the trans- 117 three-dimensional ray statisticalbin encoding model, together with in Focal length f 2000 mm of time-bin qubit analyzers using standard interferometers. mitter output, the root-mean-square variation a-,, of the 88 where δ(α) #l tan(α)/[1 tan(α)] is the lateral offset be- unbalanced interferometer (Method 2), as shown in Fig. 2(f). 144 some experimental results. The sensitivity of his angle of polarization 0 induced by atmospheric turbu- FIG. 1. Time-bin-based0 quantum communication in a turbulent measurements was limited by the equipment used, to Obscuration 187 mm Free-Space? lence is given by These interference challenges are overcome by utilizing 118 -42 dB in the daytime and -45 dB at night. No f 571 5 = + depolarization-corresponding to time- or space-aver- 1 (An2)'/2 l 1 − . free-space channel. When a time-bin-encoded photon, whose path is aged fluctuations of the polarization angle of a linearly = - 1'/2 >,) (1) 89 tween the two rays coming from each path of the interferometer The combination of glass and mirror produces a virtual mirror 145 polarized laser beam-was found at a propagation spectral filter also have large field of view, which means that thef 2 spread of incident angles −216.395 - [J. Jin, S. Agne, J.P. Bourgoin, Y. Zhang, N. Lutkenhaus, T. Jennewein, arXiv:1509.07490, relay optics in the long arm of the unbalanced Michelson 119 if we follow the theory of StrohbehmFig. and 3. Clifford Sketch [Ref. of a2015 polarized / Vol. 54, No. ray 3 / pathAPPLIEDthrough OPTICS a Cassegrain range of 2.6 km. In agreement with his theory, it must Fig. 4. Measurement error, induced by a Cassegrain telescope Fig. 6. Depolarization coefficient of a Newtonian telescope coated deviated by- Phys. atmospheric Rev. A 97, 043847 turbulence (2018)] as well as telescopes misalign- be much smaller as long as turbulence is the only source 5, Eq. (9) ]. An is themay deviation be of therelatively index of refrac- large (e.g., approximately 1° full-angle for the LaRCN HSRL-2 instrument). 0.877 6.479i of depolarization. tion of the atmosphere from itstelescope. mean, normalized to with an aluminum coating, changes with the parameter da; c with silver over the‡ wavelength range of 355–950 nm; F number of 120 unity; is the scale factor of the gaussian approxima- 90 at the output beam splitter [see Fig. 1]. From Eq.interferometer (1), we (Method 1). The idea is to reverse differences 146 Because of the fact that the above-mentioned theoret- complex refractive index of the coatings N is 0.877 6.479i. the telescope is 2–8. ment, enters a time-bin receiver with variable angle of incidence α,a situated closer to the interferometer beam splitter. With the ical predictions are contradictory, which is shown in tion of the three-dimensionalExpanding spectral density of thesinθ0 we get ‡ index of refraction used, and may be considered to be in the evolution of spatial modes over the length #l in the 121 the correlation length [Ref. 5, Eq. (31) ]; X is the wave- 20 January 2015 / Vol. 54, No. 3 /aluminum APPLIED coating OPTICS at 0.83 m. 393 From Fig. 7, the larg- lateral offset δ(α)occursbetweenthepaths(redandblueline)atthe length; L is the range of propagation.stable, Assuming and can An 2 obtain high quality spectral discrimination [4, 12, 13]; however,4. Polarization absorption Effects and Correction of Different μ 91 147 The author is with the Astronomisches Institut der Universitdt est measurement error can be found at 0.83 m. k is see that a nonzero AOI introduces path distinguishability and appropriate choice of refractive index and glass length, we Tdbingen, Waldhauserstrasse 64, Ttibingen 74, Germany. = 10-12 and = 10 cm, correspondingfilters to are strong not tur- photon efficient and there are no absorptiondd lines at manyTelescopes convenient laser μ 122 Received 6 August 1968. bulence near the ground, we find when X = 632.8 nm 2 12 calculated when the F number of the telescope is 2 8. long arm, as shown in Fig. 2(c).Thiseffectivelyguarantees Wndnd=−−2( ) sinθ ( − ) Besides coatings, the telescope s Mueller matrix is – interferometer exit. This is due to the receiver length asymmetry and 44 wavelengths. Field-widened 11interferometers 2 2 [14, 15] are 0 of high efficiency and can be built to ’ The lesser value of k can45 be found in the telescope February 1969 / Vol. 8, No. 2 / APPLIED OPTICS 367 related with system configuration and its character- any desirable laser wavelength. Applications, such as measuringnn12 Doppler linewidths [15], with a lower F number, but the difference induced 92 rapidly modulates the interferometer phase at the sameidentical time. wavefrontcan evolutions match in the the short distance and long beam-splitter-to-virtual-mirror paths of 123 to the 148 istic parameters, such as curvature of reflector, F reduces the interference quality, resulting in lower distinguishability demonstrate they can be adopted as the interferometric spectral filter for HSRL system. , (7) by the F number is small and can be neglected. 46number, and so on. Metal coating optical constants The value of k pertinent to the silver coating is less 124 A compact, robust, quasi-monolithic tiltedsin field-widenedθ00dd Michelsonsin interferometerchangeθ withdd wavelength(MI) is [16], so a telescope s Mueller of the time-bin states in superposition bases. Turbulence-induced the interferometer. Consequently, spatial indistinguishability 12 12 ’ than the aluminum coating over the wavelength 93 149 under development as the spectral discrimination−−−− filter() for a second-generationmatrix HSRL(HSRL- () will change⋯⋯ with wavelength. The Mueller The relative phase between the two paths is very sensitive to corresponding distance of the real mirror in the short arm. This 33 55 range of 0.3 0.47 m. There is a greater depolariza- 2) at National Aeronautics and Space Administration4 nn (NASA) Langley8matrices Researchnn of a Center Newton telescope and a Cassegrain – μ is restored regardless of spatial mode and AOI of the input 125 12 12 tion coefficient of k at 0.47 0.95 m for the silver spatial-mode distortions further lower the interference visibility (see telescope coated with aluminum and silver were cal- – μ 5 (LaRC). The MI consists of a cubic beam splitter, a solid arm and an air arm. Piezo stacks coating. At visible and near-infrared wavelengths 94 150 culated over the wavelength range of 0.3–0.95 m. the AOI, with a predicted π-shift per 2 10− degrees input effectively balances the interferometer. More specifically, let us connect the air arm mirror to the body of the interferometer allowing the interferometer to be μ of 0.47 0.95 m, there is less polarization crosstalk text for details). beam. For verification, we set #l 0.60 m (2.0 ns) and 126 The value of k changes with the parameters of the – μ and wetuned can within find a smallthat, spectralthe OPD range. is The power widened series field ofof view the makes sine thesquared optical path incident angle. In order tofor the silver coating. telescope and laser wavelength. × = The depolarization coefficients of a Cassegrain measure interference visibilities by applying voltages to a piezo 127 enlargedifference the field (OPD) of of view, the filter we vary can slowly let withthe incidentsecond angle term and be allows zero,Figures the collectionthat5 and is6 show of the curves of the depolariza- 95 angle variation. In order to quantify interference degradation consider the situation in which an input beam enters the inter- 151 telescope with aluminum and silver coatings over light over a large angle. In this paper, the system performance is analyzedtion over coefficient several types of a Newton telescope coated with an the wavelength range of 0.3 0.95 m are shown of system imperfections, such as cumulative wavefront error, locking error,aluminum reflectance and of a the silver layer in lidar applications, – μ mounted on a mirror in the short path, allowing it to change the 128 in Fig. 8. For a Cassegrain telescope coated with dn11//0.−= dn 2 2 over the wavelength range of 0.3–0.95 m. The(8) val- 96 152 US006115121A beam splitter and anti-reflection coatings, system tilt, and depolarization angle. The μ aluminum, its depolarization coefficients are all ap- due79 toII. input-angle MULTIMODE fluctuations,TIME-BIN ANALYZER we compute METHODS the interference ferometer with an angle of α.Theopticalpathdifferenceinthe ues of k change greatly with wavelength, and it 129 United States Patent [19] [11] Patent Number: 6,115,121requirements of each imperfection for good interferometer performance are obtained. proximately equal to 1. That is to say, the depolari- phase of the interferometer at various AOIs. Having a single- Erskine [45] Date of Patent: *Sep.Then 5, 2000 this system would be independent of incident reachesangle theto extreme third valueorder at the and wavelength have ofan about OPD This paper is constructed as follow: Section 2 makes a detailed description of the field- zation of a Cassegrain telescope can be neglected in 0.83 μm for the aluminum layer, for the reason 97 130 153 [54] SINGLE AND DOUBLE SUPERIMPOSING S. Gidon and G. Behar, “Multiple—linebetween laser Doppler velociwidened the Michelsontwo arms interferometric as spectral filter and provides the definition of the polarization measurements of the atmosphere. For a visibility.80 Considering a single-mode Gaussian beammode beam with as an input,interferometer we obtain an isinterference given by visibility#l 2(n l cos α n l cos α ), INTERFEROMETER SYSTEMS metry,” Applied Optics, vol. 27, No. 11, pp. 2315—2319, that there is the greatest optical constant of the Let us consider an unbalanced Michelson interferometer L L L S S S 1988. Cassegrain telescope coated with silver, there are [75] Inventor: David J. Erskine, Oakland, Calif. Pierre Connes, “DeuXieme Journee D’Etudes Sur Les InterTransmission Ratio that can be used to evaluate the performance of the Michelson spectral single ferences,” Revue D’Optique Theorique Instrumentale, vol. = 131 − [73] Assignee: The Regents of the University of of 0.91 0.01, which remains constant as the AOI 35, p. 37, Jun. 1956. filter in HSRL; Section 3 shows the principle of 4 the prototype tilted field-widened6 MI for 81 California, Oakland, Calif. 98 with long and short paths of lengths lL and lS,respectively. Book by Eugene Hecht and Alfred Zaj ac, “Optics,” Addison sin θ0 dd12sin θ0 dd12 intensity I and a beam width σ at the interferometer input, where n and α denote refractive index and reflection 154 [*] Notice: This patent is subject to a terminal dis Wesley, Reading Massachusetts, pp. 307—309, 1976. HSRL; the system performances of the interferometer are analyzed over different system 0 V = ± L(S) L(S) claimer. Wndnd=−−2( ) ( −− ) ( − )⋯⋯ (9) David J. Erskine and Neil C. Holmes, “White Light Veloc 11 2 2 33 55 is varied [see Fig. 2(d)]. The visibility and error are extracted 132 ity,” Nature, vol. 377, pp. 317—320, Sep. 28, 1995. imperfections in Section 4, which is followed by discussions in Section 5, and finally, some 82 While the path-length difference for zero-angle incidence [21] Appl. No.: 08/963,682 David J. Erskine and Neil C. Holmes, “Imaging White Light 4 nn12 8 nn12 [22] Filed: Oct. 31, 1997 VISAR,” Proceedings of 22nd International Congressconclusions on are given in Section 6. New Configuration with99 Symmetric Imaging Paths High—speed Photography and Photonics, October 1996. the visibility is given by [22] angle from a mirror in path l ,respectively.UsingSnell’s 155 [51] Int. Cl.7 ...... G01B 9/02 from a sinusoidal fit of measured data. The improvement isL(S)133 [52] US. Cl...... 356/345; 356/285; 356/352 83 is simply #l 2(l l ), a nonzero AOI translates into Primary Examiner—Samuel A. Turner 0 L S Multi[58] Field of Search ...... - .. 356/345,mode 346, Michelson2. Field-widenedth Michelson spectral Interferometers filter for HSRL 356/351, 352, 357, 359, 28.5 Attorney, Agent, or Firm—John P.where Wooldridge; Alan H. the 4 and higher terms can be omitted when θ is small. Note that one can obtain a Thompson = − further confirmed by measurements with a multimode beam 134 [56] References Cited [57] ABSTRACT 2.1 Michelson interferometer 84 an angle-dependent path length and a lateral offset as the law and Taylor’s expansion, the difference is approximated 156 U.S. PATENT DOCUMENTS Used in applications for multiInterferometers Which-mode can imprint supera coherent images delay onfield-widened a in Doppler Michelson-LIDAR Velocimetry filter by adding with incoherentmore glasses light [18]. sources, Astronomy, multi 5,642,194 6/1997 Erskine ...... 356/345 broadband uncollimated beam are described. The delay value can be independent of incident ray angle, alloWing 2 135 OTHER PUBLICATIONS The MI is one of the best known interferometers in optical testing and has been adopted for multimode fiber 50/50 beam splitter mirror lens [Fig. 2(b)]wherethehighvisibilityof 0.89 0.01 Narrowband Filters in LIDARinterferometry using uncollimated beams from common 85 beam propagates. Using geometrical ray tracing through the 2 Rernhard Beer, “Remote Sensing by Fourier Transform extended sources such as lamps and ?ber bundles,Figure and 3 shows the incident angle dependence of OPD for an ordinary Michelson facilitating Fourier Transform spectroscopy of Wide anglemany applications [16, 17]. It consists of a 50/50 beam splitterspectral and twofilter arms also havewith large a mirror field ofat view, which means that the spread of incident angles #l tan(α) Spectrometry,” John Wiley & Sons, NeW York, 1992, spectral filter also have large field of view, which means that the spread of incident angles 0 n l n Vl = α± l /n l /n 157 sources. Pairs of such interferometers matched in delay and as 2( ) sin ( )forsmallangles QD96.F68B415, p. 17. L L S S L 136L S S P. Connes, “L’Etalon de Fabry—Perot Spherique,” Le Journal dispersion can measure velocity andinterferometer communicate usingeach end. The (blue input beamstar) isand directed a field-widened intomay the be system relatively and largeonemay produces (e.g., be (pinkrelatively approximately two largediamond) outputs, (e.g., 1° full-angle approximately as arethat for the 1°has LaRC full-angle theHSRL-2 forsame instrument).the LaRC original HSRL-2 instrument). • [Fig. 2(e)]demonstratesthattheinterferometerdesignisrobust ordinary lamps, Wide diameter optical ?bers and arbitrary Observed interference 86 SuperimposingDe Physique et le Radium, 19, pp. 262—269,Interferometers 1958. Field-Widened Michelson Interferometers Appl. Opt. 11(3), 507–516 (1972). interferometer, we find that the path-length difference is given R. L. Hilliard and G. G. Shepherd, “Wide Angle Michelson non-imaging paths, and not requiring a laser. spectral filter also have large field of view, which means that the spread of incident angles (α) exp , (2) indicated by Output I and II in Fig. 2. Expanding sinθ weExpanding get sinθ0 we get 0 − − − Interferometer for Measuring Doppler Line Widths,” J. Opt. OPD (150mm) and works at the same wavelength0may be(355nm). relatively large As (e.g., is approximately shown 1°in full-angle Fig. for3(a), the LaRC the HSRL-2 OPD instrument). Soc. Am., vol. 56, No. 3, pp. 362—369, Mar. 1966. 32 Claims, 34 Drawing Sheets Appl. Opt. 24(11), 1571–1584 (1985) against highly distortedα beams.α This is noteworthy as it allows 137 158 Expanding sinθ we get dd visibilities of >97 % in both 87 by V = V − √ L and S.Withaproperchoiceofrefractiveindicesfor 0 dd 2 12 σ α 2 2 [1 tan( )] 12 suffers a change of more than 60 λ for the ordinaryWndnd=−−2( MI )Wndnd sinwith=−−2(θ (11 the − 2 ) 2 )incident sinθ 0 ( − angle ) at 1 degree SM. 11 2 2 0 nn 138 AM. Fig. 5. Calibrationnn12 parameter of12 a Newtonian telescope coated % & ' ( us to couple the output of the interferometer into a multimode \\\\ 2 dd12 , (7) 88,57 while the OPD of the field-widened MI is very constant Wndndover=−−2( a large )46 sin rangeθ ( − of ) incident, (7) angle. + with46 aluminum11 over 2 2sin theθ wavelengthdd 0 rangesin θ of 0.3dd–0.95 μm (the Fig. 7. Measurement error, induced by aoutputs, Newton telescope with both paths, we can remove the second term so that #l 159 sin θ00dd12sin θ 00dd 1212nn 12 −−−−F number() of the telescope−−−− is ()() 2–8); we12 assume⋯⋯ that () the laser⋯⋯ polari- an aluminum coating, changes with the parameter da over the 33 5533 55 , (7) #l 1 1 tan(α) fiber, yielding a high coupling efficiency of 0.87 for delivery of 139 Figure 3(b) shows a detail illustration of the incident angle dependence446nn of the8 field-widenednn 0 zation4 isnn aligned12 to thesin8xθaxisnndd1212 in the coordinatesin θ systemdd12 in Fig. 1. wavelength range of 0.28–0.83 μm. −−−−00()12 () 12⋯⋯ #l(α) − 33 55 100 where denotes the system visibility at zero AOI. For 160 MI and the discussed field-widenedand MI we can encounters find that,and the we OPD can an findis power OPDthat, seriesthe OPDchange of theis powersine4 squared ofseriesnn12 only ofincident the sineabout8 angle. squarednn12 In order0.068 incident to angle.λ . In order to 0 photons to the detector.becomes Phase-recovery insensitive capacity to is AOI, discussed thus140 restoring indistinguishability 394 APPLIED OPTICS / Vol. 54, No. 3 / 20 January 2015 = 2 cos(α) + cos(α) sin(α) enlarge the field of view,enlarge we the can field let theof view, second we term can letbe zero,the second that is term be zero, that is 90 For a 400mm aperture, 1mrad field of view telescope,and we can find the that, spectralthe OPD is power filter series should of the sine squaredhave incident at least angle. In order to • Average visibility of 98.5 % V ! " + in the section Measurements and Results. 141 enlarge the field ofdn view,//0.−= we dn can let the dn11 second//0.−= dn 2term 2 be zero, that is(8) (8) 101 instance, with σ 1.49 mm and #l 0.60 m, due to Eq. (2), 11 2 2 π 0 at the interferometer output. In our implementation, we use 161 16mrad if the input beam aperture is 25mm. TheThen 16mradthis system would divergence be independent ofangle, incident angleor toabout third order 0.92 and have an OPD Then this system would be independent of incident angledn//0. to−= third dn order and have an OPD (8) for the 4 QKD states. Delaying Mirror Assembly 11 2 2 δ(α)tan α , (1) 142 degree, is too large for ordinary MI tobetween act the as two spectral armsbetween as the filter, two arms but as it will not pose a problem for a = = The second type of interferometer we study is based on the Then this system would be independent of incident angle to third order and have an OPD 102 4 4 6 the visibility will+ drop to 0.70− for α 0.1 and 0.91. The Erskine, US Patent 6,115,121 (2000) between the two arms4 as sin6 θ dd sin θ dd ◦ 0 118 mm-long glass with the refractive index n 1.4825 in 162 field-widened MI. Fig. 2. Ray diagram of Michelson interferometer. sin θ0 dd12sin θ00 dd1212 0 12 use of media with different refractive indices for the paths of the 143 Wndnd=−− 2( )Wndnd=−−2(11 ( −− 2 2 ) ) ( (33 − −− ) )⋯⋯ (55(9) − )⋯⋯ (9) 11 2 2 33 55 (b) # $ 4 nn 844 nnnn12 86 nn12 = V = 12 sin θ dd12sin θ dd When the incident angle θ is zero, the above shown interferometerWndnd =−− is2( an ordinary ) 0 (12 −− )0 (12 − )⋯⋯ (9) = 0 th 11 2 2 33 55 103 relationship88 where δ(α) Eq.#l (tan(2)isverifiedexperimentallywithasingle-α)/[1 tan(α)] is the lateral offset be- 144 th • Photon collection into a 0 unbalanced interferometer (Method 2), as shown in Fig. 2(f). 163 where the 4 and higherwhere termsthe 4 can and be higher omitted terms when can θ be is omitted4small.nn 12Note when that θ isone 8small. cannn 12 obtainNote that a one can obtain a the long path and none in the short path, providing an optical Michelson interferometer and the irradiance TI at the Output Isuper can befield-widened expressed Michelson as filter by adding more glasses [18]. = + super field-widened whereMichelson the 4 filterth and by higher adding terms more can glasses be omitted [18]. when θ is small. Note that one can obtain a 89 145 Figure 3 shows theFigure incident 3 shows angle the dependence incident angle of OPD dependence for an ordinary of OPD Michelson for an ordinary Michelson multimode fiber of 80 %, tween the two rays coming from each path of the interferometer The combination of glass and mirror produces a virtual mirror super field-widened Michelson filter by adding more glasses [18]. 104 mode beam [see Fig. 2(a)], generated by a continuous-wave TItrI =+2[1cos2]000interferometerπ W (blue interferometer star) and a field-widened (blue star) and one (a1) (pinkfield-widened diamond) one that (pink has thediamond) same original that has the same original path-length difference of #l 0.17 m (0.57 ns). Interference 164 OPDFigure (150mm) 3 showsand works the at incident the same angle wavelength dependence (355nm). of OPDAs is forshown an in ordinary Fig. 3(a), Michelson the OPD 90 at the output beam splitter [see Fig. 1]. From Eq. (1), we situated closer to the interferometer beam splitter. With the 146 OPD (150mm) and worksinterferometer at the same (blue wavelength star) and a(355nm). field-widened As is shown one (pink in Fig. diamond) 3(a), the that OPD has the same original where, I is the irradiance of input beam, sufferst and a changer are ofsuffers more the absolute thana change 60 λ transmittanceoffor more the ordinary than 60 λ andMI for with the theordinary incident MI angle with atthe 1 incidentdegree angle at 1 degree from input to output! = 0 0 0 whileOPD (150mm)the OPD andof the works field-widened at the same MI wavelength is very constant (355nm). over As a islarge shown range in Fig.of incident 3(a), the angle. OPD 105 laser at 776 nm. For instance, as shown in Fig. 2(d),theini- 165 while the OPD of thesuffers field-widened a change MIof moreis very than constant 60 λ forover the a largeordinary range MI of with incident the incident angle. angle at 1 degree 91 see that a nonzero AOI introduces path distinguishability and appropriate choicevisibilities of refractive index of 0.94 and glass0.01 length, [see we Fig.147 2(g)]and0.90 0.01 [see reflectance coefficients of the beam splitter andFigure W 3(b)is the shows OPD aFigure detail of the 3(b)illustration two shows arms aof detail thein theincident illustration unit angle of of dependencethe incident ofangle the field-wideneddependence of the field-widened wavelength. MIwhile and the the OPD discussed of the field-widened MI isencounters very constant an OPD over changea large rangeof only of aboutincident 0.068 angle.λ . single MI and the discussedFigure field-widened 3(b) shows MI a detailencounters illustration an OPD of thechange incident of only angle about dependence 0.068 λ of. the field-widened 92 rapidly modulates the interferometer phase at the same time. can match the distance beam-splitter-to-virtual-mirror± to the 148 ± For a 400mm aperture,For a1mrad 400mm field aperture, of view 1mrad telescope, field theof viewspectral telescope, filter should the spectral have atfilter least should have at least In a similar way, the irradiance TII at the Output II is MI and the discussed field-widened MI encounters an OPD change of only about 0.068 λ . 106 tial interference visibility of 0.91 0.01 decreases Fig. 2(h)]aremeasuredwithasingle-modeandmultimode 166 16mrad if the input beam aperture is 25mm. The 16mrad divergence angle, or about 0.92 0 16mrad if the inputFor beam a 400mm aperture aperture, is 25mm. 1mrad The field 16mrad of view divergence telescope, angle, the spectralor about filter 0.92 should have at least 93 Figure 2. Measured interference visibilities with 149 Liu et al, degree,Vol. 20, is No.too large 2 / OPTICSdegree,for ordinary is EXPRESS too MI large to actfor1406 asordinary spectral (2012) MI filter, to act but as it spectral will not filter, pose buta problem it will notfor posea a problem for a The relative phase between the two paths is very sensitive to corresponding distance of the real mirror in the short arm. This 16mrad if the input beam aperture is 25mm. The 16mrad divergence angle, or about 0.92 V multimode= beam (inset)± while varying incidence Erskine, Holmes, Nature, Vol 377, p317 (1995) field-widened MI. field-widened MI. 107 5 167 degree, is too large for ordinary MI to act as spectral filter, but it will not pose a problem for a rapidly94 the AOI, with with AOI. a predicted Theπ same-shift per laser 2 10 beam(a) −and rotationdegrees (b) is angles. theninput senteffectively through balancesbeam, the interferometer. respectively, More specifically, which remain let us 150 constant as the AOI is varied. #156591 - $15.00 USD Received 17 Oct 2011; revised 28 Nov 2011; acceptedfield-widened 21 Dec 2011; MI. published 9 Jan 2012 × (C) 2012 OSA 16 January 2012 / Vol. 20, No. 2 / OPTICS EXPRESS 1408 108 a95 multimodeangle variation. fiber, In order thereby to quantify distorting interference degradationit into a multimodalconsider the situationHence, in which correcting an input beam optics enters the not inter- only151 improves performance at 168 96 due to input-angle fluctuations, we compute the interference ferometer with an angle of α.Theopticalpathdifferenceinthe 152 46 48 109 beam [23] which mimics the effect of turbulent atmosphere higher AOI but is also necessary to enable high interference 169 97 visibility. Considering a single-mode Gaussian beam with interferometer is given by #l 2(nLlL cos αL nSlS cos αS), 153 = − Fig. 3. Comparison of OPD incident angle dependence between ordinary and field-widened 110 [Fig.98 intensity2(b);see[I0 and a1 beam,17]forcomparison].Despitelengthyand width σ at the interferometer input, where nL(S) and αL(S)visibilitydenote refractive with a index multimode and reflection beam.154 170 Michelson interferometers, (a) incident angle dependence comparison, (b) detailed illustration © 1995 Nature Puofblis htheing G rperformanceoup of the field-widened MI. 99 the visibility is given by [22] angle from a mirror in path lL(S),respectively.UsingSnell’s 155

Fig. 3. Comparison of OPDFig. 3. incident Comparison angle ofdependence OPD incident between angle ordinary dependence and field-widened between ordinary and field-widened law and Taylor’s expansion, the difference is approximated 156 Michelson interferometers,Michelson (a) incident interferometers, angle dependence (a) incident comparison, angle dependence (b) detailed comparison, illustration (b) detailed illustration Fig. 3. Comparison of OPD incident angle dependence between ordinary and field-widened 2 2.3 Transmission ratio of the Michelson spectralof the performance filter of theof field-widened the performance MI. of the field-widened MI. 2 Michelson interferometers, (a) incident angle dependence comparison, (b) detailed illustration #l0 tan(α) 003800-2 157 of the performance of the field-widened MI. as 2(nLlL nSlS) sin α(lL/nL lS/nS)forsmallangles Figure 4 shows a schematic diagram2.3 of Transmission the field-widened ratio2.3 ofTransmission the Michelson ratioMichelson spectral of the Michelsonfilter spectral spectral filter filter for spectral (α) 0 exp , (2) − − − F2.3igure Transmission 4 shows a schematicratio of the diagram Michelson of the spectral field-widened filter Michelson spectral filter for spectral αL and αS.Withaproperchoiceofrefractiveindicesfor 158 discrimination in HSRL system. TheFigure backscatter 4 shows a schematic signal diagram whichof the field-widened contains Michelson backscatter spectral filter for fromspectral the V = V − √2σ [1 tan(α)] discrimination in HSRLdiscriminationFigure system. 4 shows The in a schematicHSRL backscatter system. diagram signal The of whichbackscatter the field-widened contains signal backscatter which Michelson contains from spectral the backscatter filter for from spectral the % & + ' ( 6 discrimination in HSRL system. The backscatter signal which contains backscatter from the both paths, we can remove the second term so that #l 159 100 where 0 denotes the system visibility at zero AOI. For becomes insensitive to AOI, thus restoring indistinguishability 160 #156591 - $15.00 USD #156591Received - $15.00 17 Oct USD 2011; revisedReceived 28 17Nov Oct 2011; 2011; accepted revised 2128 DecNov 2011; 2011; published accepted 219 Jan Dec 2012 2011; published 9 Jan 2012 (C) 2012 OSA 16 January 2012 / Vol. 20, No. 2 / OPTICS EXPRESS 1410 V (C) 2012 OSA #156591 - $15.00 USD Received16 January 17 Oct 2012 2011; / Vol. revised 20, 28 No. Nov 2 / 2011;OPTICS accepted EXPRESS 21 Dec 1410 2011; published 9 Jan 2012 101 instance, with σ 1.49 mm and #l0 0.60 m, due to Eq. (2), at the interferometer output. In our implementation, we use 161 #156591 - $15.00 USD Received 17 Oct 2011; revised (C)28 2012 Nov OSA 2011; accepted 21 Dec 2011;16 January published 2012 / Vol. 20, 9No. Jan 2 / OPTICS 2012 EXPRESS 1410 = = (C) 2012 OSA 16 January 2012 / Vol. 20, No. 2 / OPTICS EXPRESS 1410 102 the visibility will drop to 0.70 for α 0.1◦ and 0 0.91. The 118 mm-long glass with the refractive index n 1.4825 in 162 = V = = 103 relationship Eq. (2)isverifiedexperimentallywithasingle- the long path and none in the short path, providing an optical 163 104 mode beam [see Fig. 2(a)], generated by a continuous-wave path-length difference of #l 0.17 m (0.57 ns). Interference 164 = 105 laser at 776 nm. For instance, as shown in Fig. 2(d),theini- visibilities of 0.94 0.01 [see Fig. 2(g)]and0.90 0.01 [see 165 single ± ± 106 tial interference visibility of 0.91 0.01 decreases Fig. 2(h)]aremeasuredwithasingle-modeandmultimode 166 V0 = ± 107 rapidly with AOI. The same laser beam is then sent through beam, respectively, which remain constant as the AOI is varied. 167 108 a multimode fiber, thereby distorting it into a multimodal Hence, correcting optics not only improves performance at 168 109 beam [23] which mimics the effect of turbulent atmosphere higher AOI but is also necessary to enable high interference 169 110 [Fig. 2(b);see[1,17]forcomparison].Despitelengthyand visibility with a multimode beam. 170

003800-2 7/31/20

Outdoor Time-Bin QKD Channel Towards free-space MDI-QKD

• 1.2 km outdoor link • No trust on the central Bell-state measurement • Introduced additional turbulence • Ideally, the BSM would be located on the moving • also introduced depolarization Systems, such as airplanes or satellites. • • Full BB84 protocol Challenge: The time-of-flight for each channel will be Hoi-Kwong Lo group, Physical Review variable Letters 112(19), 2013 2

Time (s) 0 50 100 150 200 250 300 1600 H R 1400 | ⟩ | ⟩ V | ⟩ 1200

Range (km) L | ⟩ 1000

20 Det H Vallone et al.Det PRL,H 2014 Det L Det L 10 | ⟩ | ⟩ | ⟩ | ⟩ J. Jin et al., OPTICS EXPRESS, 27(26):37214–37223, 2019. 0

Counts 10 Det V Det V Det R Det R 20 | ⟩ | ⟩ | ⟩ | ⟩ 49 54 −2 −1 0 1 2 −2 −1 0 1 2 −2 −1 0 1 2 −2 −1 0 1 2 ∆ = tmeas− tref (ns)

FIG. 2. Top: Larets trajectory measured by the 10 Hz SLR pulses. The four selected 10 s intervals correspond to four different polarization input states. Bottom: the four histograms report the obtained counts at the receiver for each single photon detector in function of the measured detection time tmeas, demonstrating an average QBER of 6.5 %. The signal on the two detectors is blue for H/L polarization and green for V/R. Gray dashed lines represent the 1 selection interval around the expected time of arrival tref .

the qubits encoded in four different polarization states, cor- satellite motion with respect to the ground. Our detection ac- responding to two mutually unbiased basis. A secret key can curacy was set equal to the detector time jitter (0.5 ns), as be established between the transmitter (Alice, at the satellite) other contributions to time uncertainties coming from detec- andGoal: the receiver (Bob,Extract at MLRO) the when the synchronization average Quan- tion electronics or of laser Alice fluctuations areand negligible. Counts 1 Challenge tum Bit Error Rate (QBER) is below 11% . In a transmis- registered within 1 interval around tref were considered as sionBob with polarization only qubits, after the QBERthe can be measurements estimated as signal, while the background is estimated from the counts out- Q =(nwrong+1)/(ncorr+nwrong+2) where ncorr and nwrong side 3 . Details of the setup are described in Supplementary • are the number of detections in the sent and orthogonal polar- Material. How to synchronize the wave packets • Combination2 of DV and CV MDI-QKD, bring out the best of both emitted by Alice, Bob, such that they ization respectively . The exploitation of CCRs with metallic QCs of polarized photons QCs using generic polarization coatingworlds: on the three reflecting faces is crucial for preserving states from two mutually unbiased bases were realised with a interfere on Charlie’s beam splitter? the imposed polarization state during the reflection. For this • Photon Detection from Discrete Variable singleSchemes passage allows of Larets. for The channels passage waswith divided in four in- reason we could not use satellites mounting uncoated or di- tervals of 10 s in which we sent horizontal H , vertical V , • With a moving systems, a real-time long distances / high transmission losses | i | i electric coated CCRs. We selected five LEO (Low Earth Or- circular left L and circular right R states. At the receiver 2 000 | i | i compensation is challenging. bit, below• Longkm) coherence satellites: Jason-2,wave packets Larets, Starlette, inspired and bythe Continuous state analysis isVariables performed Schemes, by two single photon detec- • Alice-Charlie, and Bob-Charlie, must Stella withoffer metallic ability coated for CCRs Alice, and Ajisai,Bob, Charlie with uncoated to operatetors measuringalmost independently two orthogonal polarizations, from which the independently measure the exact round CCRs, for comparison. QBER is extracted. The results are summarized in FIG. 2. In trip time for their channels, and actively In order to reject the background and dark counts, a pre- the four intervals, we obtained 199 counts in the correct de- compensate for any changes. cise synchronization at Bob is needed. For this purpose we tector and 13 wrong counts, giving an average QBER of 6.5 exploited the satellite laser ranging (SLR) signal. The latter is %. Once considered the average 3.6 % duty cycle of our setup • This measurement requires two-way S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T.10 Gehring, generated in a much coarser comb of strong pulses ( Hz rep- (see SupplementaryMeasure Material), Now the mean return frequency in propagation of synchronization information Hoi-Kwong Lo group, Physical Review C. S.etition Jacobsen, rate U. L. andAndersen,100 HighmJ-rate pulse measurement energy)-device whose-independent seed quantum is taken from Letters 112(19), 2013 cryptography, Nat. Photon. 9, p. 397-402, 2015. the selected intervals is 147 Hz. (a-la Einstein) the same comb used for the qubits. Two non-polarizing beam Ulrik L. Andersen, Tobias Gehring, Christian S. Jacobsen and Stefano Pirandola, Effective measurement- Analyze Later devicesplitters-independent were quantum used cryptography, in the SPIE Newsroom optical. DOI: path 10.1117/2.1201509.006119 in order to merge and A further analysis has been carried out to prove the preser- split the outgoing and incoming SLR signal and qubit stream vation of the polarization state for the other coated satellites. (see FIG. 1). For qubits discrimination, we synchronized the These results will prove that low QBERs can be obtained in state analyser with the time-tagging of SLR pulses provided different conditions and satellite orbit, showing the stability by the MLRO unit, which has few picosecond accuracy. In- and the reliability of our approach. We will also report the 55 56 deed, by dividing the intervals between two consecutive SLR detection rates achievable with the different LEO satellites. In detections in 107 equidistant subintervals, we determined the this analysis we divided the detection period in intervals of 5 sequence of expected qubit times of arrival tref . This tech- seconds: for each interval the data were analyzed only if the nique compensates for the time scale transformation due to signal of at least one detector was 5 standard deviations above the background. The QBERs resulting from this analysis are shown in FIG. 3 for Ajisai, having non polarization preserving 1 By using the post-selection techniques introduced in [22], QBER up to CCRs, and for the polarization preserving satellites Jason-2, 20% can be tolerated for secret key generation. Larets, Starlette and Stella. We achieved a QBER below 10 % 7 2 We used the Bayesian estimator of the QBER. for several tens of seconds in all the polarization maintaining 7/31/20

Triangular HOM Interference Time-resolved HOM

HOM coincidences sorted based on modulation timing.

Measure Now Analyze Later

S. Agne PhD thesis, Aug. 2018. S. Agne PhD thesis, Aug. 2018. S. Agne et al, arXiv:2004.11259 [quant-ph], accepted in Optics Express, 2020. S. Agne et al, Optics Express, 2020.

59 60

Entanglement over global distances via quantum repeaters with satellite links

1 2 2 1, 3, 2, 4, 1, K. Boone, J.-P. Bourgoin, E. Meyer-Scott, K. Heshami, ⇤ T. Jennewein, † and C. Simon ‡ 1Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary T2N 1N4, Alberta, Canada 2Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada 3National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, K1A 0R6, Canada 4Quantum Information Science Program, Canadian Institute for Advanced Research, Toronto, ON, Canada We study entanglement creation over global distances based on a quantum repeater architecture that uses low-earth orbit satellites equipped with entangled photon sources, as well as ground Research on Quantum Networks Global Quantumstations equipped with quantum Networks? non-demolition detectors and quantum memories. We show that this approach allows entanglement creation at viable rates over distances that are inaccessible via direct transmission through optical fibers or even from very distant satellites. • Efficient and robust q-channels • A hybrid between satellite links and quantum repeatersOver the last may few decadesachieve the distributionoverall best of quan- Satellite(source) • Dimensions – power – mass tum entanglement has progressed from tabletop exper- performance 2 • chip scale systems ? iments to distances of over one hundred kilometers [1]. h Will it be possible to create entanglement over global works. Terrestrial free-space QKD is ultimately range • Satellites and Q-Repeaters

QND QND QND QND QND QND Earth • Interfaces / transducers limited by the Earth’s curvature and the method is suit- distances? This is interesting from a fundamental point able mainly for intra- and inter-city links [20, 21]. In of• view,Distances but also fromup to the 20,000 perspective km of trying to create Ground station • connect channels with stationary qubits satellite QKD (SatQKD) [22, 23], the transmission loss QM QM QM QM QM QM through the vacuum of space is dominated by di↵rac- a global “quantum internet” [2]. In the context of quan- L tion that has an inverse square scaling instead of expo- tum cryptography, it would enable secure global commu- 0 BSM • Long term q-memories nential. However, the connection distance for SatQKD nication without having to rely on anyK. Boone, trusted Bourgoin nodes [3],, Meyer-Scott, Heshami, TJ, Simon. PRA 91, 052325 (2015) is primarily limited by the line-of-sight between satellite as entanglement is the foundation for device-independent FIG. 1. (Color online) Proposed quantum repeater architec- • Routing technologies and ground station which in turn depends on its orbit ture with satellite links. Each elementary link (of length L ) unless the satellite acts as a trusted node [24–29]. To es- quantum key distribution [4]. It would also be useful for 0 consists of an entangled photon pair source on a low-earth tablish a global quantum network without trusted nodes global clock networks [5] and for very long baseline tele- • Cost will require overcoming the above limitations. The use orbit satellite (at height h), and two ground stations consist- of quantum satellites equipped with quantum memories scopes [6]. ing of quantum non-demolition (QND) measurement devices as quantum repeaters remains relatively unexplored. Modern classical telecommunication relies on optical and quantum memories (QM). The successful transmission In this paper, we develop and characterise new ap- QND fibers. Unfortunately the directQND transmissionDaniel Oi, of Strathclyde photons Group:of entangled Study photonson Quantum to each Memories ground station on Satellites, is heralded by proaches for global QKD using space and ground net- works. Our approach exploits satellites equipped with QM through fibers is not practicalQM forMustafa quantum Gündogan communi-, et al,the arXiv:2006.10636v1 QND devices, which detect the presence of a photon62 non- quantum memories to provide free-space optical repeater cation over global distances because losses are too high. destructively and without revealing its quantum state. The links to connect two end stations on the ground. We im- The best available fibers have a loss of 0.15 dB/km at the entanglement is then stored in the memories until informa- plement memory-assisted measurement-device indepen- FIG. 1. Top: Hybrid QND-QR protocol, following [35]with tion about successful entanglement creation in two neighbor- 61 62nesting level, n =1andsegmentlength,L0.Entangledpho- dent QKD (MA-QKD) protocols [30–32] to achieve high optimal wavelength. This means, for example, that the ing links is received. Then the entanglement can be extended rates and device-independent security on board satellites ton pairs are created by on-board sources (pink stars) and sent to ground stationstime to (I). distribute After a QND one detection entangled heralds photon pair over 2000 in a line-of-sight setting. The entanglement distribution by entanglement swapping based on a Bell state measurement the arrival of thekm photons with they a 1 are GHz loaded source to QMs exceeds (II). BSM the age of the universe. (BSM). Figure 2 shows that four to eight such links are su- rate is used as a benchmark to assess the performance of is performed between the memories to extend entanglement our repeater chain. Our approach overcomes limitations between end stationsTwo (III). alternative Bottom: New approaches architecture where to try to overcome this cient for spanning global distances. in purely ground-based repeater networks and trusted the QND and QMsproblem are also located are currently on-board an being orbiting pursued satel- in parallel, namely satellite relays to provide the best rate-loss scaling for lite. quantum communications over planetary scales. Notably, fiber-based quantum repeaters and direct satellite links. we demonstrate that satellites equipped with QMs pro- Conventional quantum repeaters rely on first creating source has been announced for 2016 [20]. The advantage vides three orders of magnitude faster entanglement dis- The first generationand storing of QRs entanglement rely on the postselection for elementary links, then ex- of quantum communication via satellites is that trans- tribution rates over global distances than existing pro- of entanglement, which acts as an entanglement dis- 8 tocols. For connecting ground-based networks, we show tillation operation.tending Improved the distance generations of of entanglement QRs may by entanglement mission loss is dominated by di↵raction rather than ab- that QMs can increase key rates for general line-of-sight employ active errorswapping correction [7, 8]. codes Based that on necessitate the experimental and theo- sorption and thus scales much more favorably with dis- distance QKD protocols. Our work provides a practical shorter link distances and higher number of qubits (50-

arXiv:1410.5384v1 [quant-ph] 20 Oct 2014 retical progress in this area over the last few years, it tance. For example, consider a pair source on a satellite roadmap towards an implementation of global commu- 100, i.e. a quantum computer in the Sycamore scale) per nication, navigation and positioning, and sensing. We node. Hence, weis restrict plausible our thatattention this to approach the first gen- will make it possible to at a height of 1000 km. For realistic assumptions (such as conclude by providing meaningful benchmarks to the per- eration type architecturesextend the that distance employ of ensemble-based entanglement distribution signifi- telescope size, see below), the combined transmission loss formance of QMs for di↵erent tasks and propose di↵erent QMs. The usecantly of atomic beyond ensembles what for is possible long-distance with direct transmission for the photon pair for a 2,000 km ground station distance architectures for the light-matter interface. communication was first proposed in a seminal paper by Duan, Lukin, Ciracthrough and Zolleroptical [15 fibers] also [8–10]. known as However, the truly global dis- is only of order 40 dB. This should be contrasted with 300 DLCZ protocol.tances It relies are on stillcreating very photon-spin dicult waveto envision for repeaters dB for a fiber link of the same length. However, global II. QUANTUM REPEATER AND entanglement throughbased Ramanon fiber scattering. links. This This is proto- true also for related ap- distances are still challenging even for satellite links. Di- MEMORY-ASSISTED QKD PROTOCOLS col has been modified and improved significantly over time [16, 33, 34proaches]. Nevertheless, based entanglement on quantum distribu- error correction [11], which rect transmission from low-earth orbit (LEO) satellites, We first outline two QR protocols for global entangle- tion rate with thesetend schemes to require quickly repeater drops below stations practi- that are only a few kilo- i.e. those below the Van Allen radiation belt, or up to ment distribution followed by MA-QKD protocols in up- cally useful levelsmeters above apart. few thousand kilometers which link and downlink configurations to increase the keyrates renders reaching true global distances a formidable chal- about 2000 km in height, no longer works. Even before in a quantum communication within the line-of-sight dis- lenge with land-basedThe architectures. use of satellite links for quantum communication the Earth gets in the way, the loss becomes forbidding for tance of the satellite. Here, QMs are used as quantum A hybrid, satellite-assistedis also being architecture pursued very has actively.been pro- There has been a lot very grazing incidence due to long propagation distance storage devices to increase the rate of otherwise proba- posed for entanglementof progress distribution in terms with usefulof feasibility rates [35] studies [12–19]. The in air. One possible solution is to use satellites that are bilistic Bell state measurements (BSMs) that form the (Fig. 1, top). It relies on satellites equipped with entan- backbone of most MDI protocols. gled photon pairlaunch sources of communicating the first satellite with the carrying mem- an entangled pair much further away, but this comes at significant cost, as ory nodes located in ground stations. Other than the satellite links the main di↵erence it exhibits with respect A. Quantum repeaters to other first generation protocols is that heralding is performed via a quantum non-demolition (QND) mea- QRs can be grouped into di↵erent architectures depend- surement. Entanglement is then distributed between the ing on the error correction mechanism employed [17]. communicating parties via entanglement swapping oper- 7/31/20

Long-term vision for fundamental science multimode fiber 50/50 beam splitter mirror lens • J. Jin et al., OPTICS EXPRESS, 27(26):37214–37223, (2019). Summary • J. Jin, et al. Phys. Rev. A 97, 043847 (2018) • Global Quantum Networks with satellites • Quantum • We need to understand all (fundamental) effects that are going on in order to get desired behavior Communication in Space • C. Pugh et al, Quantum Science and Technology, 2, 2, 024009 (2017) • QEYSSat mission • Question of unification of quantum theory and • Exploring new relativity directions for robust • R. Tannous, APPLIED PHYSICS • We need to explore regimes with large (relativistic) velocities LETTERS, 115(21), (2019). and speeds, and gravitational influences. Free-Space Quantum • Test the interplay of quantum mechanics and gravity ? Communications: • Time-bin Review of possible science test for quantum entanglement in space: • RFI-QKD • S. Agne et al, Optics Express, (2020). Fundamental quantum optics experiments conceivable with • • K. Boone, et al. PRA 91, 052325 (2015) satellites-reaching relativistic distances and velocities towards MDI-QKD • J.P. Bourgoin, et al, NJP, 15:023006, (2013). D. Rideout, T.J, et al. Class. Quant. Grav., 29(22):224011 , 2012. 63 65

Thank You

Program Member Annual Report 2011 04-07-11 11:04

Last Saved: 07/04/2011 11:04 AM

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First name Thomas

Last name Jennewein

E-mail address [email protected]

66 Country where you Canada normally live and Postdoc and Graduate Positions available! work Province Ontario

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