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Probl. Peredachi Inf., 2010, Volume 46, Issue 3, Pages 3–21 (Mi ppi2018)  

This article is cited in 12 scientific papers (total in 12 papers)

Information Theory

Mutual and coherent information for infinite-dimensional quantum channels

A. S. Holevo, M. E. Shirokov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The paper is devoted to the study of quantum mutual information and coherent information, two important characteristics of a quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are given, and their properties are studied in detail. Basic identities relating the quantum mutual information and coherent information of a pair of complementary channels are proved. An unexpected continuity property of the quantum mutual information and coherent information, following from the above identities, is observed. An upper bound for the coherent information is obtained.

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English version:
Problems of Information Transmission, 2010, 46:3, 201–218

Bibliographic databases:

UDC: 621.391.1+519.7
Received: 28.01.2010
Revised: 07.06.2010

Citation: A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Probl. Peredachi Inf., 46:3 (2010), 3–21; Problems Inform. Transmission, 46:3 (2010), 201–218

Citation in format AMSBIB
\by A.~S.~Holevo, M.~E.~Shirokov
\paper Mutual and coherent information for infinite-dimensional quantum channels
\jour Probl. Peredachi Inf.
\yr 2010
\vol 46
\issue 3
\pages 3--21
\jour Problems Inform. Transmission
\yr 2010
\vol 46
\issue 3
\pages 201--218

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    This publication is cited in the following articles:
    1. A. A. Kuznetsova, “Conditional entropy for infinite-dimensional quantum systems”, Theory Probab. Appl., 55:4 (2011), 709–717  mathnet  crossref  crossref  mathscinet  isi
    2. Furrer F., Åberg J., Renner R., “Min- and max-entropy in infinite dimensions”, Comm. Math. Phys., 306:1 (2011), 165–186  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Shirokov M.E., “Entropy reduction of quantum measurements”, J. Math. Phys., 52:5 (2011), 052202, 18 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Wu Zh., Zhang Sh., Zhu Ch., “Quantum Jensen-Shannon Divergence Between Quantum Ensembles”, Appl. Math. Inf. Sci., 6:3 (2012), 509–514  mathscinet  isi  elib
    5. A. A. Kuznetsova, “Inverse coding theorem for infinite-dimensional quantum channels”, Moscow University Mathematics Bulletin, 68:1 (2013), 48–52  mathnet  crossref  mathscinet
    6. 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
    7. 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
    8. Muller-Hermes A., Reeb D., “Monotonicity of the Quantum Relative Entropy Under Positive Maps”, Ann. Henri Poincare, 18:5 (2017), 1777–1788  crossref  mathscinet  zmath  isi  scopus
    9. Alpay D., Jorgensen P., Levanony D., “On the Equivalence of Probability Spaces”, J. Theor. Probab., 30:3 (2017), 813–841  crossref  mathscinet  zmath  isi  scopus
    10. Wilde M.M. Qi H., “Energy-Constrained Private and Quantum Capacities of Quantum Channels”, IEEE Trans. Inf. Theory, 64:12 (2018), 7802–7827  crossref  mathscinet  zmath  isi  scopus
    11. Sharma K. Wilde M.M. Adhikari S. Takeoka M., “Bounding the Energy-Constrained Quantum and Private Capacities of Phase-Insensitive Bosonic Gaussian Channels”, New J. Phys., 20 (2018), 063025  crossref  isi  scopus
    12. Lim Y. Takagi R. Adesso G. Lee S., “Activation and Superactivation of Single-Mode Gaussian Quantum Channels”, Phys. Rev. A, 99:3 (2019), 032337  crossref  mathscinet  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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