Zero-error channel capacity and simulation assisted by non-local correlations

Specifically, when the channel being simulated is noiseless, this reduces to the zero-error capacity of the channel, assisted by the various classes of non-signalling correlations. ... For assistance by arbitrary non-signalling correlations, linear programming formulas for capacity and simulation are derived, the former being equal (for channels with non-zero unassisted capacity) to ... ACKNOWLEDGMENTS We would like to thank Nicolas Brunner, Runyao Duan, Tsuyoshi Ito, Ashley Montanaro, Marcin Pawłowski, Paul Skrzypczyk and Stephanie Wehner for useful discussions. ...

doi:10.1109/tit.2011.2159047 fatcat:w3um3pdz3fal3d25il22gjlj5m

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In this case, a particularly elegant theory results and, remarkably, it is sometimes possible to transmit information with zero-error using a channel with no unassisted zero-error capacity. ... We investigate the connection between this phenomenon and that of "pseudo-telepathy" games. The use of generalised non-signalling correlations to assist in this task is also considered. ... Non-signalling assisted zero-error capacity and exact simulation. ...

doi:10.1103/physrevlett.104.230503 pmid:20867220 fatcat:vc2pdmzb5jhirjb6ulcclthn2q

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We study the one-shot zero-error classical capacity of a quantum channel assisted by quantum no-signalling correlations, and the reverse problem of exact simulation of a prescribed channel by a noiseless ... The zero-error classical capacity is given by a similar-looking but different SDP; the asymptotic zero-error classical capacity is the regularization of this SDP, and in general we do not know of any simple ... We study the one-shot zero-error classical capacity of a quantum channel assisted by quantum no-signalling correlations, and the reverse problem of exact simulation of a prescribed channel by a noiseless ...

doi:10.1109/tit.2015.2507979 fatcat:ltm4yjbcvfdqhcmqn3opkxwpsy

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More specifically, we consider scenarios with as little purification as possible and we show that for sufficiently low local losses, such purifications are still more powerful than multiplexing. ... We present a detailed rate analysis for a hybrid quantum repeater assuming perfect memories and using optimal probabilistic entanglement generation and deterministic swapping routines. ... We study the one-shot zero-error classical capacity of quantum channels assisted by quantum non-signalling correlations, and the reverse problem of exact simulation. ...

doi:10.1103/physreva.83.012323 fatcat:wenw4zgrpnhqxls2jjytqghawq

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In this case, Bob can simulate the complementary channel from A to E by locally applying the map E . ... So, an eavesdropper (Eve), who has access to the environment of the channel, can simulate the channel from A to B by locally applying the map E. ... So, an eavesdropper (Eve), who has access to the environment of the channel, can simulate the channel from A to B by locally applying the map E. ...

doi:10.4171/news/102/4 fatcat:5vposczmqncclfwn2px7apvbne

Szczepanski

We develop the theory of α-bits, including the applications above, and determine the α-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised ... The decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification ... Acknowledgements We thank David Ding, Michael Walter and Andreas Winter for valuable discussions. This work was supported by AFOSR (FA9550-16-1-0082), CIFAR and the Simons Foundation, ...

arXiv:1706.09434v2 fatcat:zr7obfoatbei7cnw2kjg646ph4

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Our findings give new insight into this non-additivity of the channel capacity and its relation to quantum privacy. ... channel using a shared quantum state as a key, then the insecure quantum channel is only ever used to simulate a symmetric-side channel, and can always be replaced by it without altering the optimal rate ... Then the distillable entanglement, secret-key capacity, and weak mutual independence capacity (zero-way, one-way, assisted by erasure channel, by a symmetric-side channel, or by any other channel) are ...

doi:10.1109/tit.2012.2236911 fatcat:vvhadye5cvfnhbxrzoappgytae

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We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. ... Then we go on to show that the feedback-assisted capacity is non-zero (with constant activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number ... We thank Marcin Pawłowski and Ciara Morgan for listening with empathy to our teething problems with the mixed state cq-channels, Aram Harrow, Janis Nötzel and many others for enjoyable discussions on zero-error ...

doi:10.1109/tit.2016.2562580 fatcat:fvunsuzrtrcxxibcp3ld6tsd7m

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First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. ... of channel simulation and provides insights and bounds for the case under entanglement-assisted codes. ... MB thanks the Centre for Quantum Software and Information at the University of Technology Sydney for their hospitality while part of this work was done. ...

doi:10.1109/tit.2019.2943858 fatcat:ntyjvbdc5nabvbkbzdcfqmedi4

As we show, such expressions appear in problems of entanglement-assisted Gray-Wyner and entanglement-assisted channel simulation, where the question of whether entanglement helps in these settings is related ... In this paper, we develop a new non-Carathéodory-type tool for evaluating expressions involving a single quantum auxiliary register and several classical random variables. ... SB was in part supported by a grant from IPM (No. 91810409). AG was in part supported by a grant from IPM (No. CS1390-3-01), and the Iranian National Science Foundation No. 89003743. ...

doi:10.1109/tit.2013.2286079 fatcat:trcep3acjvbgjbisozoymnktzy

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For discrete memoryless channels, it is shown that non-signalling codes attain the channel capacity with zero error probability if and only if the dispersion of the channel is zero. ... Motivated by recent work on entanglement-assisted codes for sending messages over classical channels, the larger, easily characterised class of non-signalling codes is defined. ... ACKNOWLEDGMENTS I would like to thank Andreas Winter, Toby Cubitt and Debbie Leung for useful discussions. ...

doi:10.1109/tit.2012.2210695 fatcat:gnydxfgec5fdnp7foxh6zdfboi

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We finally study the zero-error setting and provide efficiently computable upper bounds on the one-shot zero-error capacity of a general quantum channel. ... We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability ... [83] first introduced the zero-error communication via classical channels assisted by classical no-signalling correlations. ...

doi:10.1109/tit.2017.2741101 fatcat:gtee7xaqwrhmffktjgvhwesinm

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Our results on tensor power sources establish a strong converse to the entanglement-assisted capacity theorem. ... For channels of nonzero capacity, this simulation is always possible, but for it to be efficient, auxiliary resources of the proper kind and amount are generally required. ... We believe that zero-error simulation of classical channels using optimal rates of communication requires exponential amounts of shared randomness, and that for quantum channels, zero-error simulations ...

doi:10.1109/tit.2014.2309968 fatcat:r3raa6dlvveopc3xfjf2zrjc7m

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We study a channel model for multipath wireless channel and exploit the channel diversity in generating secret key bits. ... We design and analyze a method to extract secret keys from the randomness inherent to wireless channels. ... OFDM simulation results We first show the simulation result of an IEEE 802.11a channel. We simulate the frequency and sampled channel coefficients and their correlation matrices. ...

doi:10.1109/tifs.2012.2206385 fatcat:rylwew4txzhgndbkxvglpa6brm

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In this paper we overview the properties of the quantum communication channel, the various capacity measures and the fundamental differences between the classical and quantum channels. ... For quantum communication channels, many new capacity definitions were developed in comparison to classical counterparts. ... Acknowledgement The results discussed above are supported by the grant TAMOP-4.2.2.B-10/1--2010-0009 and COST Action MP1006. ...

arXiv:1208.1270v5 fatcat:sfpzwo3yrbebrgdqlo64l5c7ea

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Zero-Error Channel Capacity and Simulation Assisted by Non-Local Correlations

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Improving Zero-Error Classical Communication with Entanglement

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No-Signalling-Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovász Number

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Rate analysis for a hybrid quantum repeater

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Selected Advances in Quantum Shannon Theory

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Approximate Quantum Error Correction Revisited: Introducing the Alpha-bit [article]

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Public Quantum Communication and Superactivation

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On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback

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Quantum Channel Simulation and the Channel's Smooth Max-Information

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On Dimension Bounds for Auxiliary Quantum Systems

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A Linear Program for the Finite Block Length Converse of Polyanskiy–Poor–Verdú Via Nonsignaling Codes

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Semidefinite Programming Strong Converse Bounds for Classical Capacity

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The Quantum Reverse Shannon Theorem and Resource Tradeoffs for Simulating Quantum Channels

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Exploiting Channel Diversity in Secret Key Generation From Multipath Fading Randomness

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Properties of the Quantum Channel [article]

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