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Probl. Peredachi Inf., 2012, Volume 48, Issue 2, Pages 3–20 (Mi ppi2072)  

This article is cited in 7 scientific papers (total in 7 papers)

Information Theory

Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel

M. E. Shirokov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow

Abstract: Several relations between the Holevo capacity and entanglement-assisted classical capacity of a quantum channel are proved; necessary and sufficient conditions for their coincidence are obtained. In particular, it is shown that these capacities coincide if (respectively, only if) the channel (respectively, the $\chi$-essential part of the channel) belongs to the class of classical-quantum channels (the $\chi$-essential part is a restriction of a channel obtained by discarding all states that are useless for transmission of classical information). The obtained conditions and their corollaries are generalized to channels with linear constraints. By using these conditions it is shown that the question of coincidence of the Holevo capacity and entanglement-assisted classical capacity depends on the form of a constraint. Properties of the difference between quantum mutual information and the $\chi$-function of a quantum channel are explored.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00139-а
Russian Academy of Sciences - Federal Agency for Scientific Organizations

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English version:
Problems of Information Transmission, 2012, 48:2, 85–101

Bibliographic databases:

UDC: 621.391.1+519.2
Received: 06.09.2011
Revised: 21.03.2012

Citation: M. E. Shirokov, “Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel”, Probl. Peredachi Inf., 48:2 (2012), 3–20; Problems Inform. Transmission, 48:2 (2012), 85–101

Citation in format AMSBIB
\by M.~E.~Shirokov
\paper Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a~quantum channel
\jour Probl. Peredachi Inf.
\yr 2012
\vol 48
\issue 2
\pages 3--20
\jour Problems Inform. Transmission
\yr 2012
\vol 48
\issue 2
\pages 85--101

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    This publication is cited in the following articles:
    1. A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31  mathnet  crossref  isi
    2. A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14  mathnet  crossref  mathscinet  isi
    3. M. E. Shirokov, “Criteria for equality in two entropic inequalities”, Sb. Math., 205:7 (2014), 1045–1068  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. S. Holevo, M. E. Shirokov, “On the Gain of Entanglement Assistance in the Classical Capacity of Quantum Gaussian Channels”, Math. Notes, 97:6 (2015), 974–977  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. K. Kononenko, “An Approach To Error Correction in Program Code Using Dynamic Optimization in a Virtual Execution Environment”, J. Supercomput., 72:3 (2016), 845–873  crossref  isi  scopus
    6. M. E. Shirokov, A. S. Holevo, “On lower semicontinuity of the entropic disturbance and its applications in quantum information theory”, Izv. Math., 81:5 (2017), 1044–1060  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. Sh. Kananizadeh, K. Kononenko, “Development of Dynamic Protection Against Timing Channels”, Int. J. Inf. Secur., 16:6 (2017), 641–651  crossref  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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