DOCSLIB.ORG

Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback Dawei Ding∗, Yihui Queky, Peter W. Shorz, and Mark M. Wildex ∗Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA, [email protected] yInformation Systems Laboratory, Stanford University, Stanford, California 94305, USA, [email protected] zCenter for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA, [email protected] xHearne Institute for Theoretical Physics, Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA, [email protected] Abstract—We prove that the classical capacity of an arbitrary strong converse statement in [6], [7]. Bowen et al. proved quantum channel assisted by a free classical feedback channel is that the capacity of an entanglement-breaking channel for bounded from above by the maximum average output entropy sending classical messages is not increased by a free classical of the quantum channel. As a consequence of this bound, we conclude that a classical feedback channel does not improve feedback channel [8], and this result was strengthened to a the classical capacity of a quantum erasure channel, and by strong converse statement in [9]. Ref. [10] discussed several taking into account energy constraints, we conclude the same inequalities relating the classical capacity assisted by classical for a pure-loss bosonic channel. The method for establishing the feedback to other capacities. At the same time, it is known that aforementioned entropy bound involves identifying an informa- in general there can be an arbitrarily large gap between the tion measure having two key properties: 1) it does not increase under a one-way local operations and classical communication unassisted classical capacity and the classical capacity assisted channel from the receiver to the sender and 2) a quantum channel by classical feedback [11]. from sender to receiver cannot increase the information measure Our aim here is to go beyond [8] to establish an upper bound by more than the maximum output entropy of the channel. This on the classical capacity of an arbitrary, not just entanglement- information measure can be understood as the sum of two terms, breaking, quantum channel assisted by a classical feedback with one corresponding to classical correlation and the other to entanglement. channel. Due to the fact that a quantum feedback channel is a stronger resource than a classical feedback channel, an I. INTRODUCTION immediate consequence of Bowen’s result [2] is that the A famous result of Shannon is that a free feedback channel entanglement-assisted capacity is an upper bound on the does not increase the capacity of a classical channel for classical capacity assisted by classical feedback. However, communication [1]. That is, the feedback-assisted capacity is since a quantum channel can, in general, establish quantum equal to the channel’s mutual information. Shannon’s result entanglement [12]–[14] and entanglement can increase capac- indicates that the mutual information formula for capacity ity [3]–[5], in such cases it may appear difficult to establish is particularly robust, in the sense that, a priori, one might an upper bound on this capacity other than the entanglement- consider a feedback channel to be a strong resource for assisted capacity. Our main result is that the latter is actually assisting communication. possible: we prove here that the maximum output entropy of With the rise of quantum information theory, several re- a quantum channel is an upper bound on its classical capacity arXiv:1902.02490v2 [quant-ph] 15 Jul 2019 searchers have found variations and generalizations of Shan- assisted by classical feedback. As a generalization of this non’s aforementioned result, in the context of communication result, we find that the maximum average output entropy is over quantum channels. For example, Bowen proved that the an upper bound on the same capacity for a channel that is a capacity of a quantum channel for sending classical messages, probabilistic mixture of other channels. when assisted by a free quantum feedback channel, is equal The approach that we take for establishing the aforemen- to the channel’s entanglement-assisted capacity [2], which tioned bounds is similar in spirit to approaches used to bound is in turn equal to the mutual information of a quantum other assisted capacities or protocols [15]–[18]. We identify channel [3]–[5]. This result indicates that the mutual infor- an information measure that has two key properties: 1) it mation of a quantum channel is robust, in a sense similar does not increase under a free operation, which in this case to that mentioned above. The result also indicates that the is a one-way local operations and classical communication best strategy, in the limit of many channel uses, is to use the (1W-LOCC) channel from the receiver to the sender, and 2) quantum feedback channel once in order to establish sufficient a quantum channel from sender to receiver cannot increase shared entanglement between the sender and receiver, and the information measure by more than the maximum output to subsequently employ an entanglement-assisted communi- entropy of the channel. This information measure can be cation protocol [3]–[5]. Bowen’s result was strengthened to a understood as the sum of two terms, with one corresponding to classical correlation and the other to entanglement. W We organize the rest of the paper as follows. Section II provides a formal definition of a protocol for classical com- A’ A’ A’ A’ munication over a quantum channel assisted by classical F A B F A B F A B feedback. Section III discusses explicitly how to purify such N N N Ŵ a protocol, which is an important conceptual step for our B’ B’ B’ analysis. Section IV introduces our key information measure and several important supplementary lemmas regarding it. Fig. 1. A protocol for classical communication over three uses of a quantum Section V then employs this information measure and the sup- channel NA!B , when assisted by a classical feedback channel. plementary lemmas to establish the maximum output entropy bound for classical capacity assisted by classical feedback. We 0 apply this bound to the erasure channel and pure-loss bosonic Bob processes his systems B1B1 with the decoding chan- 1 channel in Section VI. We conclude in Section VII. nel 0 0 and Alice acts with the encoding channel B1B1!F1B2 2 D A0 F !A0 A , resulting in the state II. PROTOCOL FOR CLASSICAL COMMUNICATION OVER A E 1 1 2 2 QUANTUM CHANNEL ASSISTED BY CLASSICAL FEEDBACK (2) 2 1 (1) ! 0 0 ( 0 0 0 0 )(ρ 0 0 ): WA A B A F1!A A2 B1B !F1B WA B B 2 2 2 ≡ E 1 2 ◦ D 1 2 1 1 1 To begin with, let n; M N, let " [0; 1], and let E 0. (5) 2 2 ≥ Let A!B be a quantum channel, and let H be a Hamiltonian This process iterates n 2 more times, resulting in the N − acting on the input system A of A!B. An (n; M; H; E; ") following states: N protocol for classical communication over a quantum channel (i) (i) ρWA0 B B0 Ai!Bi (!WA0 A B0 ); (6) A!B consists of n uses of the quantum channel A!B, i i i ≡ N i i i N N along with the assistance of a classical feedback channel from (i+1) !WA0 A B0 the receiver Bob to the sender Alice, in order for Alice to send i+1 i+1 i+1 ≡ i+1 i (i) one of M messages to Bob such that the error probability is ( 0 0 0 0 )(ρ 0 0 ); (7) A Fi!A Ai+1 BiBi!FiBi+1 WA BiB no larger than ". Furthermore, the average state at the input of E i i+1 ◦ D i i each channel use should have energy no larger than E, when for i 2; : : : ; n 1 . The final decoding (measurement) channel2 fn −resultsg in the following state: taken with respect to the Hamiltonian H. B B0 !W^ D n n In more detail, the protocol consists of an initial classical– n (n) 0 0 0 ρ ^ (TrA 0 )(ρ 0 0 ): (8) quantum state σF B , with F0 classical and B quantum, of W W n BnB !W^ WAnBnBn 0 1 1 ≡ ◦D n the form Figure 1 depicts the above protocol for n = 3. X f0 0 For an (n; M; H; E; ") protocol, the following is satisfied σF0B = p(f0) f0 f0 F0 σB0 : (1) 1 j ih j ⊗ 1 f 1 0 Φ ^ ρ ^ "; (9) 2 W W − W W 1 ≤ It also involves n encoding channels, with each one denoted 1 PM i where ΦW W^ M m=1 m m W m m W^ is by A0 F !A0 A for i 1; : : : ; n , as well as n decoding ≡ j ih j ⊗ j ih j i−1 i−1 i i the maximally classically correlated state. Note that E 2 f g i channels, with each of them denoted by 0 0 for 1 BiB !FiB Φ ρ = Pr W^ = W W D i i+1 2 W W^ W W^ 1 , where here denotes i 1; : : : ; n 1 . Note that all F systems are classical the uniform− random variablef 6 correspondingg to the message 2 f − g because the feedback channel is constrained to be a classical choice and W^ denotes the random variable corresponding channel. So this means that each decoding channel is a quan- ^ to the classical value in the register W of the state ρW W^ .
Load more

Recommended publications
  • Pilot Quantum Error Correction for Global
    Pilot Quantum Error Correction for Global- Scale Quantum Communications Laszlo Gyongyosi*1,2, Member, IEEE, Sandor Imre1, Member, IEEE 1Quantum Technologies Laboratory, Department of Telecommunications Budapest University of Technology and Economics 2 Magyar tudosok krt, H-1111, Budapest, Hungary 2Information Systems Research Group, Mathematics and Natural Sciences Hungarian Academy of Sciences H-1518, Budapest, Hungary *[email protected] Real global-scale quantum communications and quantum key distribution systems cannot be implemented by the current fiber and free-space links. These links have high attenuation, low polarization-preserving capability or extreme sensitivity to the environment. A potential solution to the problem is the space-earth quantum channels. These channels have no absorption since the signal states are propagated in empty space, however a small fraction of these channels is in the atmosphere, which causes slight depolarizing effect. Furthermore, the relative motion of the ground station and the satellite causes a rotation in the polarization of the quantum states. In the current approaches to compensate for these types of polarization errors, high computational costs and extra physical apparatuses are required. Here we introduce a novel approach which breaks with the traditional views of currently developed quantum-error correction schemes. The proposed solution can be applied to fix the polarization errors which are critical in space-earth quantum communication systems. The channel coding scheme provides capacity-achieving communication over slightly depolarizing space-earth channels. I. Introduction Quantum error-correction schemes use different techniques to correct the various possible errors which occur in a quantum channel. In the first decade of the 21st century, many revolutionary properties of quantum channels were discovered [12-16], [19-22] however the efficient error- correction in quantum systems is still a challenge.
    [Show full text]
  • Analysis of Quantum Error-Correcting Codes: Symplectic Lattice Codes and Toric Codes
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Caltech Theses and Dissertations Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes Thesis by James William Harrington Advisor John Preskill In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2004 (Defended May 17, 2004) ii c 2004 James William Harrington All rights Reserved iii Acknowledgements I can do all things through Christ, who strengthens me. Phillipians 4:13 (NKJV) I wish to acknowledge first of all my parents, brothers, and grandmother for all of their love, prayers, and support. Thanks to my advisor, John Preskill, for his generous support of my graduate studies, for introducing me to the studies of quantum error correction, and for encouraging me to pursue challenging questions in this fascinating field. Over the years I have benefited greatly from stimulating discussions on the subject of quantum information with Anura Abeyesinge, Charlene Ahn, Dave Ba- con, Dave Beckman, Charlie Bennett, Sergey Bravyi, Carl Caves, Isaac Chenchiah, Keng-Hwee Chiam, Richard Cleve, John Cortese, Sumit Daftuar, Ivan Deutsch, Andrew Doherty, Jon Dowling, Bryan Eastin, Steven van Enk, Chris Fuchs, Sho- hini Ghose, Daniel Gottesman, Ted Harder, Patrick Hayden, Richard Hughes, Deborah Jackson, Alexei Kitaev, Greg Kuperberg, Andrew Landahl, Chris Lee, Debbie Leung, Carlos Mochon, Michael Nielsen, Smith Nielsen, Harold Ollivier, Tobias Osborne, Michael Postol, Philippe Pouliot, Marco Pravia, John Preskill, Eric Rains, Robert Raussendorf, Joe Renes, Deborah Santamore, Yaoyun Shi, Pe- ter Shor, Marcus Silva, Graeme Smith, Jennifer Sokol, Federico Spedalieri, Rene Stock, Francis Su, Jacob Taylor, Ben Toner, Guifre Vidal, and Mas Yamada.
    [Show full text]
  • QIP 2010 Tutorial and Scientific Programmes
    QIP 2010 15th – 22nd January, Zürich, Switzerland Tutorial and Scientific Programmes asymptotically large number of channel uses. Such “regularized” formulas tell us Friday, 15th January very little. The purpose of this talk is to give an overview of what we know about 10:00 – 17:10 Jiannis Pachos (Univ. Leeds) this need for regularization, when and why it happens, and what it means. I will Why should anyone care about computing with anyons? focus on the quantum capacity of a quantum channel, which is the case we understand best. This is a short course in topological quantum computation. The topics to be covered include: 1. Introduction to anyons and topological models. 15:00 – 16:55 Daniel Nagaj (Slovak Academy of Sciences) 2. Quantum Double Models. These are stabilizer codes, that can be described Local Hamiltonians in quantum computation very much like quantum error correcting codes. They include the toric code This talk is about two Hamiltonian Complexity questions. First, how hard is it to and various extensions. compute the ground state properties of quantum systems with local Hamiltonians? 3. The Jones polynomials, their relation to anyons and their approximation by Second, which spin systems with time-independent (and perhaps, translationally- quantum algorithms. invariant) local interactions could be used for universal computation? 4. Overview of current state of topological quantum computation and open Aiming at a participant without previous understanding of complexity theory, we will discuss two locally-constrained quantum problems: k-local Hamiltonian and questions. quantum k-SAT. Learning the techniques of Kitaev and others along the way, our first goal is the understanding of QMA-completeness of these problems.
    [Show full text]
  • Reliably Distinguishing States in Qutrit Channels Using One-Way LOCC
    Reliably distinguishing states in qutrit channels using one-way LOCC Christopher King Department of Mathematics, Northeastern University, Boston MA 02115 Daniel Matysiak College of Computer and Information Science, Northeastern University, Boston MA 02115 July 15, 2018 Abstract We present numerical evidence showing that any three-dimensional subspace of C3 ⊗ Cn has an orthonormal basis which can be reliably dis- tinguished using one-way LOCC, where a measurement is made first on the 3-dimensional part and the result used to select an optimal measure- ment on the n-dimensional part. This conjecture has implications for the LOCC-assisted capacity of certain quantum channels, where coordinated measurements are made on the system and environment. By measuring first in the environment, the conjecture would imply that the environment- arXiv:quant-ph/0510004v1 1 Oct 2005 assisted classical capacity of any rank three channel is at least log 3. Sim- ilarly by measuring first on the system side, the conjecture would imply that the environment-assisting classical capacity of any qutrit channel is log 3. We also show that one-way LOCC is not symmetric, by providing an example of a qutrit channel whose environment-assisted classical capacity is less than log 3. 1 1 Introduction and statement of results The noise in a quantum channel arises from its interaction with the environment. This viewpoint is expressed concisely in the Lindblad-Stinespring representation [6, 8]: Φ(|ψihψ|)= Tr U(|ψihψ|⊗|ǫihǫ|)U ∗ (1) E Here E is the state space of the environment, which is assumed to be initially prepared in a pure state |ǫi.
    [Show full text]
  • Potential Capacities of Quantum Channels 2
    WINTER AND YANG: POTENTIAL CAPACITIES OF QUANTUM CHANNELS 1 Potential Capacities of Quantum Channels Andreas Winter and Dong Yang Abstract—We introduce potential capacities of quantum chan- Entangled inputs between different quantum channels open the nels in an operational way and provide upper bounds for these door to all kinds of effects that are impossible in classical quantities, which quantify the ultimate limit of usefulness of a information theory. An extreme phenomenon is superactivation channel for a given task in the best possible context. Unfortunately, except for a few isolated cases, potential capac- [13]; there exist two quantum channels that cannot transmit ities seem to be as hard to compute as their “plain” analogues. quantum information when they are used individually, but can We thus study upper bounds on some potential capacities: For transmit at positive rate when they are used together. the classical capacity, we give an upper bound in terms of the The phenomenon of superactivation, and more broadly of entanglement of formation. To establish a bound for the quantum super-additivity, implies that the capacity of a quantum channel and private capacity, we first “lift” the channel to a Hadamard channel and then prove that the quantum and private capacity does not adequately characterize the channel, since the utility of a Hadamard channel is strongly additive, implying that for of the channel depends on what other contextual channels are these channels, potential and plain capacity are equal. Employing available. So it is natural to ask the following question: What these upper bounds we show that if a channel is noisy, however is the maximum possible capability of a channel to transmit close it is to the noiseless channel, then it cannot be activated information when it is used in combination with any other into the noiseless channel by any other contextual channel; this conclusion holds for all the three capacities.
    [Show full text]
  • Simulation of BB84 Quantum Key Distribution in Depolarizing Channel
    Proceedings of 14th Youth Conference on Communication Simulation of BB84 Quantum Key Distribution in depolarizing channel Hui Qiao, Xiao-yu Chen* College of Information and Electronic Engineering, Zhejiang Gongshang University, Hangzhou, 310018, China [email protected] Abstract: In this paper, we employ the standard BB84 protocol as the basic model of quantum key distribution (QKD) in depolarizing channel. We also give the methods to express the preparation and measurement of quantum states on classical computer and realize the simulation of quantum key distribution. The simulation results are consistent with the theoretical results. It was shown that the simulation of QKD with Matlab is feasible. It provides a new method to demonstrate the QKD protocol. QKD; simulation; depolarizing channel; data reconciliation; privacy amplification Keywords: [4] 1. Introduction 1989 . In 1993, Muller, Breguet, and Gisin demonstrated the feasibility of polarization-coding The purpose of quantum key distribution (QKD) [5] fiber-based QKD over 1.1km telecom fiber and and classical key distribution is consistent, their Townsend, Rarity, and Tapster demonstrated the difference are the realization methods. The classical key feasibility of phase-coding fiber-based QKD over 10km distribution is based on the mathematical theory of telecom fiber[6]. Up to now, the security transmission computational complexity, whereas the QKD based on [7] distance of QKD has been achieved over 120km . the fundamental principle of quantum mechanics. The At present, the study of QKD is limited to first QKD protocol is BB84 protocol, which was theoretical and experimental. The unconditionally secure proposed by Bennett and Brassard in 1984 [1].The protocol in theory needs further experimental verification.
    [Show full text]
  • Experimental Observation of Coherent-Information Superadditivity in a Dephrasure Channel
    Experimental observation of coherent-information superadditivity in a dephrasure channel 1, 2 1, 2 3, 1, 2 1, 2 1, 2 1, 2 Shang Yu, Yu Meng, Raj B. Patel, ∗ Yi-Tao Wang, Zhi-Jin Ke, Wei Liu, Zhi-Peng Li, 1, 2 1, 2 1, 2, 1, 2, 1, 2 Yuan-Ze Yang, Wen-Hao Zhang, Jian-Shun Tang, † Chuan-Feng Li, ‡ and Guang-Can Guo 1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China 2CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, P.R. China 3Clarendon Laboratory, Department of Physics, Oxford University, Parks Road OX1 3PU Oxford, United Kingdom We present an experimental approach to construct a dephrasure channel, which contains both dephasing and erasure noises, and can be used as an efficient tool to study the superadditivity of coherent information. By using a three-fold dephrasure channel, the superadditivity of coherent information is observed, and a substantial gap is found between the zero single-letter coherent information and zero quantum capacity. Particularly, we find that when the coherent information of n channel uses is zero, in the case of larger number of channel uses, it will become positive. These phenomena exhibit a more obvious superadditivity of coherent information than previous works, and demonstrate a higher threshold for non-zero quantum capacity. Such novel channels built in our experiment also can provide a useful platform to study the non-additive properties of coherent information and quantum channel capacity. Introduction.—Channel capacity is at the heart of in- capacity [16, 17].
    [Show full text]
  • A Mathematical Elements
    A Mathematical elements The language of quantum mechanics is rooted in linear algebra and functional analysis. It often expands when the foundations of the theory are reassessed, which they periodically have been. As a result, additional mathematical struc- tures not ordinarily covered in physics textbooks, such as the logic of linear subspaces and Liouville space, have come to play a role in quantum mechan- ics. Information theory makes use of statistical quantities, some of which are covered in the main text, as well as discrete mathematics, which are also not included in standard treatments of quantum theory. Here, before describ- ing the fundamental mathematical structure of quantum mechanics, Hilbert space, some basic mathematics of binary arithmetic, finite fields and random variables is given. After a presentation of the basic elements of Hilbert space theory, the Dirac notation typically used in the literature of quantum informa- tion science, and operators and transformations related to it, some elements of quantum probability and quantum logic are also described. A.1 Boolean algebra and Galois fields n A Boolean algebra Bn is an algebraic structure given by the collection of 2 subsets of the set I = {1, 2,...,n} and three operations under which it is closed: the two binary operations of union (∨) and intersection (∧), and a unary operation, complementation (¬). In addition to there being comple- ments (and hence the null set ∅ being an element), the following axioms hold. (i) Commutativity: S ∨ T = T ∨ S and S ∧ T = T ∧ S; (ii) Associativity: S ∨(T ∨U)=(S ∨T )∨U and S ∧(T ∧U)=(S ∧T )∧U; (iii) Distributivity: S ∧ (T ∨ U)=(S ∧ T ) ∨ (S ∧ U)andS ∨ (T ∧ U)= (S ∨ T ) ∧ (S ∨ U); (iv) ¬∅ = I, ¬I = ∅,S∧¬S = ∅,S∨¬S = I, ¬(¬S)=S , for all its elements S, T, U.
    [Show full text]
  • Quantum Interactive Proofs and the Complexity of Separability Testing
    THEORY OF COMPUTING www.theoryofcomputing.org Quantum interactive proofs and the complexity of separability testing Gus Gutoski∗ Patrick Hayden† Kevin Milner‡ Mark M. Wilde§ October 1, 2014 Abstract: We identify a formal connection between physical problems related to the detection of separable (unentangled) quantum states and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum interactive proof complexity class (including BQP, QMA, QMA(2), and QSZK), there corresponds a natural separability testing problem that is complete for that class. Of particular interest is the fact that the problem of determining whether an isometry can be made to produce a separable state is either QMA-complete or QMA(2)-complete, depending upon whether the distance between quantum states is measured by the one-way LOCC norm or the trace norm. We obtain strong hardness results by proving that for each n-qubit maximally entangled state there exists a fixed one-way LOCC measurement that distinguishes it from any separable state with error probability that decays exponentially in n. ∗Supported by Government of Canada through Industry Canada, the Province of Ontario through the Ministry of Research and Innovation, NSERC, DTO-ARO, CIFAR, and QuantumWorks. †Supported by Canada Research Chairs program, the Perimeter Institute, CIFAR, NSERC and ONR through grant N000140811249. The Perimeter Institute is supported by the Government of Canada through Industry Canada and by the arXiv:1308.5788v2 [quant-ph] 30 Sep 2014 Province of Ontario through the Ministry of Research and Innovation. ‡Supported by NSERC. §Supported by Centre de Recherches Mathematiques.´ ACM Classification: F.1.3 AMS Classification: 68Q10, 68Q15, 68Q17, 81P68 Key words and phrases: quantum entanglement, quantum complexity theory, quantum interactive proofs, quantum statistical zero knowledge, BQP, QMA, QSZK, QIP, separability testing Gus Gutoski, Patrick Hayden, Kevin Milner, and Mark M.
    [Show full text]
  • AQIS16 Preface Content
    The Theory of Statistical Comparison with Applications in Quantum Information Science……………………………………………………………………….….……...………..… Introduction to measurement-based quantum computation…………………………. Engineering the quantum: probing atoms with light and light with atoms in a transmon circuit QED system…………………………………………………………….……….3 The device-independent outlook on quantum physics……………………..…...……. Superconducting qubit systems: recent experimental progress towards fault-tolerant quantum computing at IBM……………………………………...… Observation of frequency-domain Hong-Ou-Mandel interference……. Realization of the contextuality-nonlocality tradeoff with a qubit-qutrit photon pair…………………………………………………………………………………….….... One-way and reference-frame independent EPR-steering………...… Are Incoherent Operations Physically Consistent? — A Physical Appraisal of Incoherent Operations and an Overview of Coherence Measures………............................. Relating the Resource Theories of Entanglement and Quantum Coherence An infinite dimensional Birkhoff’s Theorem and LOCC- convertibility………..… How local is the information in MPS/PEPS tensor networks……………......….. Information-theoretical analysis of topological entanglement entropy and multipartite correlations ……................................................................................................ Phase-like transitions in low-number quantum dots Bayesian magnetometry... Separation between quantum Lovász number and entanglement-assisted zero-error classical capacity ………..……..............................................................………...
    [Show full text]
  • The Private Classical Capacity of a Partially Degradable Quantum Channel
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Repository of the Academy's Library The Private Classical Capacity of a Partially Degradable Quantum Channel Laszlo Gyongyosi 1 Quantum Technologies Laboratory, Department of Telecommunications Budapest University of Technology and Economics 2 Magyar tudosok krt, Budapest, H-1117, Hungary 2 MTA-BME Information Systems Research Group Hungarian Academy of Sciences 7 Nador st., Budapest, H-1051, Hungary [email protected] Abstract For a partially degradable (PD) channel, the channel output state can be used to simulate the degraded environment state. The quantum capacity of a PD channel has been proven to be additive. Here, we show that the private classical capacity of arbitrary dimensional PD channels is equal to the quantum capacity of the channel and also single-letterizes. We prove that higher rates of private classical communication can be achieved over a PD channel in comparison to standard degradable channels. Keywords: private classical capacity, partial degradation, quantum Shannon theory. 1 Introduction The existence of partially degradable (PD) channels has been recently investigated, and it was shown that PD channels exist in the world of those qudit channels that have entanglement- binding complementary channels [1]. The PD channel set involves conjugate-PD channels, which represent a subset in the conjugate degradable channels; this set was introduced by Bradler et al. [11]. The sets of more capable and less noisy quantum channels were defined by Watanabe [2], and it was further demonstrated that other, well-characterized channel sets could be defined be- yond the degradable and conjugate-degradable channels.
    [Show full text]
  • An Experimental Implementation of Oblivious Transfer in the Noisy Storage Model
    ARTICLE Received 12 Sep 2013 | Accepted 10 Feb 2014 | Published 12 Mar 2014 DOI: 10.1038/ncomms4418 An experimental implementation of oblivious transfer in the noisy storage model C. Erven1,2,N.Ng3, N. Gigov1, R. Laflamme1,4, S. Wehner3,5 & G. Weihs1,6 Cryptography’s importance in our everyday lives continues to grow in our increasingly digital world. Oblivious transfer has long been a fundamental and important cryptographic primitive, as it is known that general two-party cryptographic tasks can be built from this basic building block. Here we show the experimental implementation of a 1-2 random oblivious transfer protocol by performing measurements on polarization-entangled photon pairs in a modified entangled quantum key distribution system, followed by all of the necessary classical postprocessing including one-way error correction. We successfully exchange a 1,366 bit random oblivious transfer string in B3 min and include a full security analysis under the noisy storage model, accounting for all experimental error rates and finite size effects. This demonstrates the feasibility of using today’s quantum technologies to implement secure two-party protocols. 1 Institute for Quantum Computing and Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. 2 Centre for Quantum Photonics, H. H. Wills Physics Laboratory & Department of Electrical and Electronic Engineering, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK. 3 Center for Quantum Technologies, National University of Singapore, 2 Science Drive 3, Singapore 117543. 4 Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5. 5 School of Computing, National University of Singapore, 13 Computing Drive, Singapore 117417.
    [Show full text]