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Probl. Peredachi Inf., 2012, Volume 48, Issue 1, Pages 3–14 (Mi ppi2064)  

This article is cited in 19 scientific papers (total in 19 papers)

Information Theory

Information capacity of a quantum observable

A. S. Holevo

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow

Abstract: In this paper we consider the classical capacities of quantum-classical channels corresponding to measurement of observables. Special attention is paid to the case of continuous observables. We give formulas for unassisted and entanglement-assisted classical capacities $C$ and $C_\mathrm{ea}$ and consider some explicitly solvable cases, which give simple examples of entanglement-breaking channels with $C<C_\mathrm{ea}$. We also elaborate on the ensemble-observable duality to show that $C_\mathrm{ea}$ for the measurement channel is related to the $\chi$-quantity for the dual ensemble in the same way as $C$ is related to the accessible information. This provides both accessible information and the $\chi$-quantity for quantum ensembles dual to our examples.

Funding Agency Grant Number
Russian Foundation for Basic Research 09-01-00424
Russian Academy of Sciences - Federal Agency for Scientific Organizations


Full text: PDF file (219 kB)
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English version:
Problems of Information Transmission, 2012, 48:1, 1–10

Bibliographic databases:

UDC: 621.391.1+519.2
Received: 29.07.2011
Revised: 09.10.2011

Citation: A. S. Holevo, “Information capacity of a quantum observable”, Probl. Peredachi Inf., 48:1 (2012), 3–14; Problems Inform. Transmission, 48:1 (2012), 1–10

Citation in format AMSBIB
\Bibitem{Hol12}
\by A.~S.~Holevo
\paper Information capacity of a~quantum observable
\jour Probl. Peredachi Inf.
\yr 2012
\vol 48
\issue 1
\pages 3--14
\mathnet{http://mi.mathnet.ru/ppi2064}
\transl
\jour Problems Inform. Transmission
\yr 2012
\vol 48
\issue 1
\pages 1--10
\crossref{https://doi.org/10.1134/S0032946012010012}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000302910700001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84859825907}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. E. Shirokov, “Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel”, Problems Inform. Transmission, 48:2 (2012), 85–101  mathnet  crossref  isi
    2. A. A. Kuznetsova, A. S. Holevo, “Coding theorems for hybrid channels”, Theory Probab. Appl., 58:2 (2014), 264–285  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14  mathnet  crossref  mathscinet  isi
    4. A. A. Kuznetsova, A. S. Holevo, “Coding theorems for hybrid channels. II”, Theory Probab. Appl., 59:1 (2015), 145–154  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Berta M., Renes J.M., Wilde M.M., “Identifying the Information Gain of a Quantum Measurement”, IEEE Trans. Inf. Theory, 60:12 (2014), 7987–8006  crossref  mathscinet  isi  elib  scopus
    6. Dall'Arno M., “Accessible Information and Informational Power of Quantum 2-Designs”, Phys. Rev. A, 90:5 (2014), 052311  crossref  isi  scopus
    7. Szymusiak A., “Maximally Informative Ensembles For Sic-Povms in Dimension 3”, J. Phys. A-Math. Theor., 47:44 (2014), 445301  crossref  mathscinet  zmath  isi  elib  scopus
    8. Wilde M.M. Winter A. Yang D., “Strong Converse For the Classical Capacity of Entanglement-Breaking and Hadamard Channels Via a Sandwiched R,Nyi Relative Entropy”, Commun. Math. Phys., 331:2 (2014), 593–622  crossref  mathscinet  zmath  isi  elib  scopus
    9. Dall'Arno M., Buscemi F., Ozawa M., “Tight Bounds on Accessible Information and Informational Power”, J. Phys. A-Math. Theor., 47:23 (2014), 235302  crossref  mathscinet  zmath  isi  scopus
    10. Berta M., Renes J.M., Wilde M.M., “Identifying the Information Gain of a Quantum Measurement”, 2014 IEEE International Symposium on Information Theory (Isit), IEEE International Symposium on Information Theory, IEEE, 2014, 331–335  isi
    11. Dall'Arno M., D'Ariano G.M., Sacchi M.F., “How Much a Quantum Measurement Is Informative?”, Eleventh International Conference on Quantum Communication, Measurement and Computation (Qcmc), AIP Conference Proceedings, 1633, eds. Schmiedmayer H., Walther P., Amer Inst Physics, 2014, 150–152  crossref  isi  scopus
    12. Dall'Arno M., “Hierarchy of Bounds on Accessible Information and Informational Power”, Phys. Rev. A, 92:1 (2015), 012328  crossref  mathscinet  isi  scopus
    13. Chen W., Gao Y., Wang H., Feng Yu., “Minimum Guesswork Discrimination Between Quantum States”, Quantum Inform. Comput., 15:9-10 (2015), 737–758  mathscinet  isi  elib
    14. W. Slomczynski, A. Szymusiak, “Highly Symmetric Povms and Their Informational Power”, Quantum Inf. Process., 15:1 (2016), 565–606  crossref  mathscinet  zmath  isi  elib  scopus
    15. A. S. Kholevo, “On the classical capacity of a channel with stationary quantum Gaussian noise”, Theory Probab. Appl., 62:4 (2018), 534–551  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. Yu. Kuramochi, “Minimal Sufficient Statistical Experiments on Von Neumann Algebras”, J. Math. Phys., 58:6 (2017), 062203  crossref  mathscinet  zmath  isi  scopus
    17. Ch. Hirche, M. Hayashi, E. Bagan, J. Calsamiglia, “Discrimination Power of a Quantum Detector”, Phys. Rev. Lett., 118:16 (2017), 160502  crossref  isi  scopus
    18. Garcia-Patron R., Matthews W., Winter A., “Quantum Enhancement of Randomness Distribution”, IEEE Trans. Inf. Theory, 64:6 (2018), 4664–4673  crossref  mathscinet  zmath  isi  scopus
    19. Ruan L., Dai W., Win M.Z., “Adaptive Recurrence Quantum Entanglement Distillation For Two-Kraus-Operator Channels”, Phys. Rev. A, 97:5 (2018), 052332  crossref  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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