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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 2, Pages 359–374 (Mi tvp289)  

This article is cited in 26 scientific papers (total in 26 papers)

Entanglement-assisted capacities of constrained quantum channels

A. S. Holevo

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this paper we fill a gap in previous works by proving the conjectured formula for the classical entanglement-assisted capacity of a quantum channel with additive constraint (such as the Bosonic Gaussian channel). Our main tools are the coding theorem for classical-quantum constrained channels and a finite-dimensional approximation of the input density operators for entanglement-assisted capacity. We also give sufficient conditions under which suprema in the capacity formulas are achieved.

Keywords: quantum communication channel, classical capacity, entangled state.

DOI: https://doi.org/10.4213/tvp289

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English version:
Theory of Probability and its Applications, 2004, 48:2, 243–255

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Received: 26.11.2002

Citation: A. S. Holevo, “Entanglement-assisted capacities of constrained quantum channels”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 359–374; Theory Probab. Appl., 48:2 (2004), 243–255

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Holevo, M. E. Shirokov, “Continuous ensembles and the capacity of infinite-dimensional quantum channels”, Theory Probab. Appl., 50:1 (2005), 86–98  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. M. E. Shirokov, “Entropy characteristics of subsets of states. I”, Izv. Math., 70:6 (2006), 1265–1292  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. S. Holevo, “Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory”, Russian Math. Surveys, 61:2 (2006), 301–339  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. M. E. Shirokov, “On properties of quantum channels related to their classical capacity”, Theory Probab. Appl., 52:2 (2008), 250–276  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Ganikhodjaev N., Mukhamedov F., “On entropy transmission for quantum channels”, Appl. Math. Inf. Sci., 1:3 (2007), 275–286  mathscinet  zmath  isi
    6. M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90  mathnet  crossref  mathscinet  isi  elib
    7. A. S. Holevo, “Entanglement-Breaking Channels in Infinite Dimensions”, Problems Inform. Transmission, 44:3 (2008), 171–184  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    8. M. E. Shirokov, “On Channels with Finite Holevo Capacity”, Theory Probab. Appl., 53:4 (2009), 648–662  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. A. S. Holevo, “Information capacity of a quantum observable”, Problems Inform. Transmission, 48:1 (2012), 1–10  mathnet  crossref  isi
    10. 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
    11. 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
    12. 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
    13. 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
    14. Caruso F. Giovannetti V. Lupo C. Mancini S., “Quantum Channels and Memory Effects”, Rev. Mod. Phys., 86:4 (2014), 1203–1259  crossref  adsnasa  isi  scopus
    15. A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russian Math. Surveys, 70:2 (2015), 331–367  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. 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
    17. A. S. Holevo, M. E. Shirokov, “Criterion of weak compactness for families of generalized quantum ensembles and its applications”, Theory Probab. Appl., 60:2 (2016), 320–325  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    18. 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
    19. Winter A., “Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints”, Commun. Math. Phys., 347:1 (2016), 291–313  crossref  mathscinet  zmath  isi  elib  scopus
    20. 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
    21. 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
    22. Davis N. Shirokov M.E. Wilde M.M., “Energy-Constrained Two-Way Assisted Private and Quantum Capacities of Quantum Channels”, Phys. Rev. A, 97:6 (2018), 062310  crossref  mathscinet  isi  scopus
    23. 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
    24. 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
    25. Ding D., Pavlichin D.S., Wilde M.M., “Quantum Channel Capacities Per Unit Cost”, IEEE Trans. Inf. Theory, 65:1 (2019), 418–435  crossref  mathscinet  zmath  isi  scopus
    26. 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  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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