Direct counterfactual communication via quantum Zeno effect Yuan Caoa,b,1, Yu-Huai Lia,b,1, Zhu Caoc, Juan Yina,b, Yu-Ao Chena,b, Hua-Lei Yina,b, Teng-Yun Chena,b, Xiongfeng Mac, Cheng-Zhi Penga,b,2, and Jian-Wei Pana,b,2

aShanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China; bSynergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; and cCenter for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China

Edited by Gilles Brassard, Universite´ de Montreal,´ Montreal, Canada, and accepted by Editorial Board Member Anthony Leggett March 29, 2017 (received for review August 31, 2016) Intuition from our everyday lives gives rise to the belief that infor- First, we review the SLAZ scheme (16) briefly. The first mation exchanged between remote parties is carried by physi- ingredient is a tandem interferometer that uses a large num- cal particles. Surprisingly, in a recent theoretical study [Salih H, ber (M ) of beam splitters (BSs) with a very high reflectivity of Li ZH, Al-Amri M, Zubairy MS (2013) Phys Rev Lett 110:170502], cos2(π/2M ). Two single-photon detectors (SPDs) are placed quantum mechanics was found to allow for communication, even in the two output ports of the last BS. According to the quan- without the actual transmission of physical particles. From the tum Zeno effect, one can predict which SPD would click upon viewpoint of communication, this mystery stems from a (nonintu- Bob’s choice of either blocking the upper-side arms or allow- itive) fundamental concept in quantum mechanics—wave-particle ing the photons to pass. In general, as M approaches infinity, duality. All particles can be described fully by wave functions. the resulting success probability approaches 100%. To real- To determine whether light appears in a channel, one refers to ize direct counterfactual communication, however, this is insuf- the amplitude of its wave function. However, in counterfactual ficient, because the photon may travel through the channels communication, information is carried by the phase part of the when Bob allows them to pass. The second ingredient is the wave function. Using a single-photon source, we experimentally chained quantum Zeno effect, which is at the core of the SLAZ demonstrate the counterfactual communication and successfully scheme. In each of M outer cycle’s arms, an additional tan- transfer a monochrome bitmap from one location to another by dem interferometer is nested by using N BSs with a reflectiv- using a nested version of the quantum Zeno effect. ity of cos2(π/2N ) to form the inner cycles. Hence, there are in total (M − 1)(N − 1) interferometers in the scheme. By combin- ing the two abovementioned ingredients, complete counterfac- quantum Zeno effect | counterfactual communication | heralded single tuality can be achieved in direct communication. That is, when photon source | quantum optics | quantum imaging M and N approach infinity, the probability of photons show- ing up in the transmission channel approaches zero. Therefore, he concept of “counterfactuality” originated from interaction- the SLAZ scheme requires an infinite number of tandem inter- Tfree measurements that were first presented in 1981 (1, 2), ferometers, which is obviously impractical. Moreover, in prac- in which the achievable efficiency was limited by a margin of tice, total visibility deteriorates exponentially with the number of 50%. Interaction-free measurements display a surprising con- interferometers used. Here, we simplify the SLAZ scheme while sequence, wherein the presence of an obstructing object (act- ing as a measuring device placed in an interferometer) can be Significance inferred without the object directly interacting with any (inter- rogating) particles. Later, the efficiency was improved to 100% (3) by using the quantum Zeno effect (4–6), wherein a physical Recent theoretical studies have shown that quantum mechan- state experiences a series of weak measurements. When the mea- ics allows counterfactual communication, even without actual surements are weak enough, the state is frozen in its initial state transmission of physical particles, which raised a heated with a high probability. This scheme was later applied to quan- debate on its interpretation. Although several papers have tum interrogation (7), quantum computation (8, 9), and quan- been published on the theoretical aspects of the subject, a tum cryptography (10–13). It can also be used for creating entan- faithful experimental demonstration is missing. Here, by using glement between distant atoms (14, 15). As for communication, the quantum Zeno effect and a single-photon source, direct counterfactuality refers specifically to cases in which information communication without carrier particle transmission is imple- is exchanged without physical particles traveling between two mented successfully. We experimentally demonstrate the fea- remote parties. Unfortunately, none of the previous schemes can sibility of direct counterfactual communication with the cur- be used for direct counterfactual communication because parti- rent technique. The results of our work can help deepen cles would appear in the channel for at least one logic state when the understanding of quantum mechanics. Furthermore, our information is transmitted. experimental scheme is applicable to other quantum technolo- However, a breakthrough in direct counterfactual quantum gies, such as imaging and state preparation. communication was made by Salih, Li, Al-Amri, and Zubairy Author contributions: Y.-A.C., C.-Z.P., and J.-W.P. conceived the research; Y.C., Y.-H.L., (SLAZ) (16) to solve this challenge, which raised a heated debate T.-Y.C., and C.-Z.P. designed the experiment; Y.C., Y.-H.L., J.Y., and H.-L.Y. performed on its interpretation and on whether full counterfactuality can research; Y.-H.L., Z.C., and X.M. analyzed data; Y.C., Y.-H.L., Y.-A.C., X.M., and J.-W.P. be maintained when a blockade is absent within a channel (17– wrote the paper; and C.-Z.P. and J.-W.P. supervised the project. 28). Although several publications are presently available regard- The authors declare no conflict of interest. ing the theoretical aspects of the subject, a faithful experimental This article is a PNAS Direct Submission. G.B. is a Guest Editor invited by the Editorial demonstration, however, is missing. Here, by using the quantum Board. Zeno effect and a single-photon source, a direct communication 1Y.C. and Y.-H.L. contributed equally to this work. without carrier particle transmission—the SLAZ scheme—has 2To whom correspondence may be addressed. Email: [email protected] or pcz@ustc. been successfully implemented. edu.cn.

4920–4924 | PNAS | May 9, 2017 | vol. 114 | no. 19 www.pnas.org/cgi/doi/10.1073/pnas.1614560114 Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 a tal. et Cao nondemolition NDM, plate; half-wave plate. HWP, quarter-wave QWP, mirror; measurement; half HM, and circulator; simple C, a in experiment, (OS) plates, switch our wave optical In and The reflection. PBSs control interfer- by to Michelson method realized polarization accurate are nested BSs biased a (B The using length. ometer. same by the scheme of SLAZ are simplified R3, and R2, (R1), 1 route paths, three detector whether on depending 1 irrin mirror by BLOCK and sin PASS of of between types mittance Two switches mirror. the used Bob removing are reflection. or BSs inserting certain Biased scheme. a SLAZ obtain simplified to of diagram Schematic (A) tion. 1. Fig. through transmitting finite without A (i.e., 1 channel). to an the equal of probability domain inter- a the with Within inner 1A. the Fig. in that infinite shown ensure as works, to as ferometer positions cycles, required inner responding the of the arms of upper-side 1A. arms Fig. the the in lower-side shown to the and cycles, respectively, cycles, outer corresponding, inner the 3, of and arms routes— 2, lower-side potential 1, three a are routes As there namely, phase. transformations, postprocessing BS data of the result in discarded is which result, detector if Otherwise, SPDs, individual three by subsequently interfer- D detected nested the is to Alice and by ometer transferred is photon single A 1A. source. single-photon heralded a polarization and nested interferometer a Michelson via properties counterfactual its preserving 0 C B A ntecs ftelgc0 o mlcdmrosi h cor- the in mirrors emplaced Bob 0, logic the of case the In Fig. in shown is scheme SLAZ simplified the of schematic A , Alice Bob Alice Bob D 1 and , ceai iga fdrc onefculqatmcommunica- quantum counterfactual direct of diagram Schematic M A M =4 M =4 eoe,rue3i rkn (C broken. is 3 route removed, BS BS D n da nefrne igepoo ilg to go will photon single a interference, ideal and 1 R R M M 2 D 3 3 2M (π/ PBS BS BS N =2 N =2 f R R lc ocue oi euto ihr0or 0 either of result logic a concludes Alice . R R N N Transmission Channel Transmission Channel 1 1 D C 2 2

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PHYSICS M1 M2 P1 MB LCPM R 2 R 3 R 1

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Fig. 2. Sketch of experimental setup. An SPDC source is used as a heralded single-photon source. The two optical paths R1 and R2 correspond to the outer cycle of the nested Zeno effect in the Michelson interferometer setup, while the paths R2 and R3 (the transmission channel) correspond to the inner cycle interferometer. Alice’s and Bob’s boxes are separated by 50 cm. D0, D1, and Dt , SPD; HWP, half-wave plate; PBS, PBS reflecting vertically polarized photons; QWP, quarter-wave plate.

after photon incidence; step 2, a photon oscillates through the unfortunately, many bits were ultimately not detected success- outer interferometer for three times; and step 3, the mirror is fully. As a result, Alice was needed to send single photons repeat- then removed so that the photon can emanate from the outer edly until a successful detection event (either D0 and Dt click- interferometer for subsequent detection by D0 or D1. Such a ing, or D1 and Dt clicking) was obtained. Subsequently, she then scheme (16) requires high-frequency emplacement and removal regularly transmitted feedback to Bob, informing him to con- of the mirror so that it can match the frequency of the photon tinue with the next bit until all 10 kilobits of information were pulse. This speed needs to be on the order of nanoseconds in transmitted. our case, which is technically challenging. As such, we use a half- In the ideal case of the SLAZ scheme with M = 4 and N = 2, mirror strategically in place of a high-speed removable mirror, the probabilities of Alice identifying correctly Bob’s logic 0 and and details on the control of M can be found in Materials and logic 1 are 85.4% and 100%, respectively. In our experiment, Methods. owing to imperfect interference of the interferometers, these To realize active choice between the two states [pass (logic 0) probabilities are reduced to 83.4% ± 2.2% and 91.2% ± 1.1%, and block [logic 1]), a liquid-crystal phase modulator (LCPM) respectively. The error rate was found to be considerably higher and a polarizing BS (PBS) are used on Bob’s side. If Bob were for logic 1. For cases in which Bob chooses pass (i.e., logic 0), to choose logic 1, the LCPM would apply a π-phase delay on errors are introduced mainly by the interference imperfections the arriving photon, which converts the polarization of photon of the last inner loop. However, when Bob chooses block (i.e., from horizontal (H ) to vertical (V ). The photon would then be logic 1), the three outer loops are chained, resulting in a rapid reflected by P1 and discarded, so that the transmission channel is decline in the overall visibility, owing to the accumulation of blocked; otherwise, the LCPM does not affect the arriving pho- errors manifesting from all three interferometers. As shown in ton. On Alice’s side, a bit 0 on the coincident detection of D0 Fig. 3, the Chinese knot bitmap is successfully transmitted from and Dt and a bit 1 on the coincident detection of D1 and Dt are Bob to Alice with high visibility. In principle, one can perform recorded. error-correction efforts in the data postprocessing stage, so that Another challenge in realizing the nested interferometer is information can be transmitted reliably in a deterministic way. maintaining a high visibility level for counterfactual communi- Moreover, the probability of Alice identifying Bob’s logic state cation, which required stability in the subwavelength order. We rightfully could be improved further by increasing the number of use an active phase stabilization technique in the experiment to interferometer cycles and enhancing their quality. suppress mechanical vibration and temperature drift. We replace There are several interesting related endeavors planned for detector Df with a phase stabilization system to run direct coun- future research in this topical domain. First, image transmission terfactual communication. Interference visibility can be main- can be extended from monochrome to grayscale, the key point of tained at 98% for several hours, and more details on phase sta- which is to insert such a switch in a state between block and pass. bilization can be found in Materials and Methods. This can be realized potentially via the emplacement of a partial- Direct counterfactual communication was demonstrated by pass switch. Whether such a process of direct communication transmitting a 100 × 100-pixel monochrome bitmap (Chinese maintains counterfactuality (when a partial-pass switch is used), knot), as shown in Fig. 3. Bit by bit, Bob controlled his LCPM however, should be considered carefully. Second, the informa- according to 10-kilobit bitmap information processed over 5 h tion transmitted in our current realization of counterfactual com- with a total channel loss of 52 dB. Because of this channel loss, munication is considered “classical.” Therefore, an interesting

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PHYSICS respectively, with an overall heralding efficiency ∼18%. As a result, the As discussed previously, with a theoretical removable mirror replaced by effective brightness of the heralding single-photon source is ∼3.6 × 106/s. a half-mirror, an ongoing challenge in this experiment is ensuring that the exit photons travel through the interferometer exactly three times (M = 4). Choosing and Controlling Proper M and N. Using a large M lowers the error We distinguish between desired and undesired photons by using spatial and rate of logic 0, which is given by 1− cos2(π/2M). A small N, however, will timing modes. Accordingly, the half-mirror is tilted at a very small angle of not increase the error rate with the presence of good interference visibil- ∼500 µrad to separate the photons experiencing different interferometer ity. On the other hand, photons need to travel the transmission channel cycles based on their angles of emergence. Only the photons that travel 2(M − 1)(N − 1) times before detection in the counterfactual communica- through the desired path are in the correct spatial mode to be coupled suc- tion. Hence, channel loss will increase with the value of M and N. In addi- cessfully with the single-mode fibers in front of D0 and D1. Meanwhile, the tion, a chained interferometer is more difficult to stabilize with larger M time delay between the photon triggers from Dt , and the detection clicks and N values. Therefore, in the experiment, we pick reasonable values of from D0 and D1 to select the desired events. M = 4 and N = 2 for demonstrating direct counterfactual communication. The desired transmission path of a photon (to be postselected) is Realization of BSs with Specified Reflectivity. Building biased BSs with spec- described as follows. First, the photon is transmitted through a half-mirror ified reflectivity is a challenging work. Alternatively, according to the SLAZ to enter a nested interferometer. Then, the photon bounces back and forth scheme (16), we use a wave plate and a PBS to realize the function of a biased within the interferometers M − 1 times; that is, it is reflected from the half- BS, as shown in Fig. 2. We aligned the optical axes of two quarter-wave plates, mirror M − 2 times. Finally, the photon is transmitted through the half- Q1 and Q2, to π/16 for M = 4, and that of a half-wave plate H1 to π/8 for mirror again and reaches the detection. Suppose the reflectivity of the N = 2, as shown in Fig. 2. The precision of wave plates alignment is <0.5◦. half-mirror is R, and its transmittance is (1 − R), ignoring absorption. There- fore, the probability of a photon traveling through the desired path is ACKNOWLEDGMENTS. We thank H. Salih, Q. Zhang, Z. Zhang, B. Zhao, and (1 − R)2RM−2, which is maximized at R = (M − 2)/M. The optimal reflectiv- X. Yuan for insightful discussions. This work was supported by National Nat- ity is therefore R = 50% for M = 4. Meanwhile, it is not difficult to see that ural Science Foundation of China Grants 61625503, 11674193, 11674309, the major penalty for such a replacement is the extra loss introduced by the and 11304302, and the Strategic Priority Research Program on Space Sci- − half-mirror, which is given by 1 − (1 − R)2RM 2. Hence, this loss is equivalent ence, the Chinese Academy of Sciences (CAS). J.Y. was supported by the to 15/16 in such a configuration, corresponding to 12 dB. Youth Innovation Promotion Association of CAS.

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