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Probl. Peredachi Inf., 2013, Volume 49, Issue 1, Pages 19–36 (Mi ppi2099)  

This article is cited in 11 scientific papers (total in 11 papers)

Coding Theory

On classical capacities of infinite-dimensional quantum channels

A. S. Holevo, M. E. Shirokov

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow

Abstract: A coding theorem for entanglement-assisted communication via an infinite-dimensional quantum channel with linear constraints is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and $\chi$-capacity of constrained channels are obtained, and conditions for their coincidence are given. Sufficient conditions for continuity of the entanglement-assisted classical capacity as a function of a channel are obtained. Some applications of the obtained results to analysis of Gaussian channels are considered. A general (continuous) version of the fundamental relation between coherent information and the measure of privacy of classical information transmission via an infinite-dimensional quantum channel is proved.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00319-а
Russian Academy of Sciences - Federal Agency for Scientific Organizations

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English version:
Problems of Information Transmission, 2013, 49:1, 15–31

Bibliographic databases:

UDC: 621.391.1+519.72
Received: 22.10.2012

Citation: A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Probl. Peredachi Inf., 49:1 (2013), 19–36; Problems Inform. Transmission, 49:1 (2013), 15–31

Citation in format AMSBIB
\by A.~S.~Holevo, M.~E.~Shirokov
\paper On classical capacities of infinite-dimensional quantum channels
\jour Probl. Peredachi Inf.
\yr 2013
\vol 49
\issue 1
\pages 19--36
\jour Problems Inform. Transmission
\yr 2013
\vol 49
\issue 1
\pages 15--31

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    This publication is cited in the following articles:
    1. A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14  mathnet  crossref  mathscinet  isi
    2. 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
    3. 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
    4. M. E. Shirokov, “Measures of correlations in infinite-dimensional quantum systems”, Sb. Math., 207:5 (2016), 724–768  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. 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
    6. M. E. Shirokov, “On the energy-constrained diamond norm and its application in quantum information theory”, Problems Inform. Transmission, 54:1 (2018), 20–33  mathnet  crossref  mathscinet  isi  elib
    7. M. M. Wilde, H. Qi, “Energy-constrained private and quantum capacities of quantum channels”, IEEE Trans. Inf. Theory, 64:12 (2018), 7802–7827  crossref  mathscinet  zmath  isi  scopus
    8. M. E. Shirokov, “Uniform finite-dimensional approximation of basic capacities of energy-constrained channels”, Quantum Inf. Process., 17:12 (2018), 322  crossref  mathscinet  isi  scopus
    9. N. Davis, M. E. Shirokov, M. M. Wilde, “Energy-constrained two-way assisted private and quantum capacities of quantum channels”, Phys. Rev. A, 97:6 (2018), 062310  crossref  isi  scopus
    10. Oskouei S.Kh., Mancini S., Wilde M.M., “Union Bound For Quantum Information Processing”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 475:2221 (2019), 20180612  crossref  mathscinet  zmath  isi  scopus
    11. Becker S., Datta N., “Convergence Rates For Quantum Evolution and Entropic Continuity Bounds in Infinite Dimensions”, Commun. Math. Phys., 374:2 (2020), 823–871  crossref  mathscinet  zmath  isi  scopus
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