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Probl. Peredachi Inf., 2018, Volume 54, Issue 1, Pages 3–23 (Mi ppi2256)  

This article is cited in 2 scientific papers (total in 2 papers)

Information Theory

Strong converse for the feedback-assisted classical capacity of entanglement-breaking channels

D. Dinga, M. M. Wildeb

a Department of Applied Physics, Stanford University, Stanford, USA
b Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University, Baton Rouge, USA

Abstract: Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by such entangled encoding schemes, but this is not always the case. In this paper, we prove that a strong converse theorem holds for the classical capacity of an entanglement-breaking channel even when it is assisted by a classical feedback link from the receiver to the transmitter. In doing so, we identify a bound on the strong converse exponent, which determines the exponentially decaying rate at which the success probability tends to zero, for a sequence of codes with communication rate exceeding capacity. Proving a strong converse, along with an achievability theorem, shows that the classical capacity is a sharp boundary between reliable and unreliable communication regimes. One of the main tools in our proof is the sandwiched Rényi relative entropy. The same method of proof is used to derive an exponential bound on the success probability when communicating over an arbitrary quantum channel assisted by classical feedback, provided that the transmitter does not use entangled encoding schemes.

Funding Agency Grant Number
Stanford University
Louisiana State University
National Science Foundation CCF-1350397
DARPA Quiness W31P4Q-12-1-0019
Supported from a Stanford Graduate Fellowship.
Supported from startup funds from the Department of Physics and Astronomy at LSU, the NSF under Award No. CCF-1350397, and the DARPA Quiness Program through US Army Research Office award W31P4Q-12-1-0019.

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English version:
Problems of Information Transmission, 2018, 54:1, 1–19

Bibliographic databases:

UDC: 621.391.1+519.72
Received: 07.07.2017
Revised: 20.10.2017

Citation: D. Ding, M. M. Wilde, “Strong converse for the feedback-assisted classical capacity of entanglement-breaking channels”, Probl. Peredachi Inf., 54:1 (2018), 3–23; Problems Inform. Transmission, 54:1 (2018), 1–19

Citation in format AMSBIB
\by D.~Ding, M.~M.~Wilde
\paper Strong converse for the feedback-assisted classical capacity of entanglement-breaking channels
\jour Probl. Peredachi Inf.
\yr 2018
\vol 54
\issue 1
\pages 3--23
\jour Problems Inform. Transmission
\yr 2018
\vol 54
\issue 1
\pages 1--19

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    This publication is cited in the following articles:
    1. Wilde M.M., “Optimized Quantum F-Divergences and Data Processing”, J. Phys. A-Math. Theor., 51:37 (2018), 374002  crossref  mathscinet  zmath  isi  scopus
    2. Seshadreesan K.P., Lami L., Wilde M.M., “Renyi Relative Entropies of Quantum Gaussian States”, J. Math. Phys., 59:7 (2018), 072204  crossref  mathscinet  zmath  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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