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Probl. Peredachi Inf., 2008, Volume 44, Issue 2, Pages 3–22 (Mi ppi1267)  

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

Information Theory

On Approximation of Infinite-Dimensional Quantum Channels

M. E. Shirokov, A. S. Holevo

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We develop an approximation approach to infinite-dimensional quantum channels based on a detailed investigation of continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair “channel, input state.” Obtained results are then applied to the problems of continuity of the $\chi$-capacity as a function of a channel, strong additivity of the $\chi$-capacity for infinite-dimensional channels, and approximating representation for the convex closure of the output entropy of an arbitrary quantum channel.

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English version:
Problems of Information Transmission, 2008, 44:2, 73–90

Bibliographic databases:

UDC: 621.391.1
Received: 11.12.2007

Citation: M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Probl. Peredachi Inf., 44:2 (2008), 3–22; Problems Inform. Transmission, 44:2 (2008), 73–90

Citation in format AMSBIB
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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. V. Yu. Protasov, M. E. Shirokov, “Generalized compactness in linear spaces and its applications”, Sb. Math., 200:5 (2009), 697–722  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218  mathnet  crossref  mathscinet  isi
    3. A. A. Kuznetsova, “Conditional entropy for infinite-dimensional quantum systems”, Theory Probab. Appl., 55:4 (2011), 709–717  mathnet  crossref  crossref  mathscinet  isi
    4. M. E. Shirokov, “The continuity of the output entropy of positive maps”, Sb. Math., 202:10 (2011), 1537–1564  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. 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
    6. M. E. Shirokov, “Schmidt Number and Partially Entanglement-Breaking Channels in Infinite-Dimensional Quantum Systems”, Math. Notes, 93:5 (2013), 766–779  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. M. E. Shirokov, “Reversibility conditions for quantum channels and their applications”, Sb. Math., 204:8 (2013), 1215–1237  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. 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
    9. 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
    10. M. E. Shirokov, “Estimates for discontinuity jumps of information characteristics of quantum systems and channels”, Problems of Information Transmission, 52:3 (2016), 239–264  mathnet  crossref  mathscinet  isi  elib
    11. 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
    12. 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
    13. Liuzzo-Scorpo P., Adessot G., “Optimal Secure Quantum Teleportation of Coherent States of Light”, Proceedings of Spie, 10358, eds. Soci C., Agio M., Srinivasan K., Spie-Int Soc Optical Engineering, 2017, UNSP 103580V  crossref  isi  scopus
    14. 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  isi  elib
    15. 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
    16. Lami L., Sabapathy K.K., Winter A., “All Phase-Space Linear Bosonic Channels Are Approximately Gaussian Dilatable”, New J. Phys., 20 (2018), 113012  crossref  isi  scopus
    17. Wilde M.M., “Entanglement Cost and Quantum Channel Simulation”, Phys. Rev. A, 98:4 (2018), 042338  crossref  mathscinet  isi  scopus
    18. 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
    19. Wilde M.M., “Strong and Uniform Convergence in the Teleportation Simulation of Bosonic Gaussian Channels”, Phys. Rev. A, 97:6 (2018), 062305  crossref  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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