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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 1, Pages 143–146 (Mi tvp3068)  

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

Short Communications

On the multiplicativity hypothesis for quantum communication channels

G. G. Amosov, A. S. Holevo

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A formulation of the multiplicativity hypothesis for quantum communication channels is given, the validity of which for parameter values $p$, arbitrarily close to 1, implies a positive solution of the fundamental additivity problem for channel capacity in quantum information theory. A proof of this hypothesis is given for depolarizing channels in the case of integer $p$.

Keywords: quantum communication channel, additivity problem for channel capacity, multiplicativity of the norms, depolarizing channel.


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English version:
Theory of Probability and its Applications, 2003, 47:1, 123–127

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Received: 02.04.2001

Citation: G. G. Amosov, A. S. Holevo, “On the multiplicativity hypothesis for quantum communication channels”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 143–146; Theory Probab. Appl., 47:1 (2003), 123–127

Citation in format AMSBIB
\by G.~G.~Amosov, A.~S.~Holevo
\paper On the multiplicativity hypothesis for quantum communication channels
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 1
\pages 143--146
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 1
\pages 123--127

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    This publication is cited in the following articles:
    1. King C., Ruskai M.B., “Comments on multiplicativity of maximal $p$-norms when $p=2$”, Quantum Inf. Comput., 4:6–7 (2004), 500–512  mathscinet  zmath  isi
    2. Amosov G.G., Man'ko V.I., “Quantum probability measures and tomographic probability densities”, Journal of Russian Laser Research, 25:3 (2004), 253–266  crossref  isi  scopus
    3. Giovannetti V., Lloyd S., “Additivity properties of a Gaussian channel”, Phys. Rev. A (3), 69:6 (2004), 062307, 9 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Matsumoto K., Shimono T., Winter A., “Remarks on additivity of the Holevo channel capacity and of the entanglement of formation”, Comm. Math. Phys., 246:3 (2004), 427–442  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. N. Datta, A. S. Holevo, Yu. M. Sukhov, “On a Sufficient Additivity Condition in Quantum Information Theory”, Problems Inform. Transmission, 41:2 (2005), 76–90  mathnet  crossref  mathscinet  zmath
    6. Giovannetti V., Lloyd S., Ruskai M.B., “Conditions for multiplicativity of maximal $l_p$-norms of channels for fixed integer $p$”, J. Math. Phys., 46:4 (2005), 042105, 23 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Watrous J., “Notes on super-operator norms induced by Schatten norms”, Quantum Inf. Comput., 5:1 (2005), 58–68  mathscinet  isi  elib
    8. Jacobs K., “General bound on the accessible information for quantum channels with noisy measurements”, Fluctuations and Noise in Photonics and Quantum Optics III, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 5846, 2005, 256–264  adsnasa  isi
    9. G. G. Amosov, “Remark on the Additivity Conjecture for a Quantum Depolarizing Channel”, Problems Inform. Transmission, 42:2 (2006), 69–76  mathnet  crossref  mathscinet  elib  elib
    10. 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
    11. Matsumoto K., “On additivity questions”, Quantum computation and information, Topics Appl. Phys., 102, Springer, Berlin, 2006, 133–164  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. King C., Koldan N., “New multiplicativity results for qubit maps”, J. Math. Phys., 47:4 (2006), 042106, 9 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. Audenaert K.M.R., “A norm compression inequality for block partitioned positive semidefinite matrices”, Linear Algebra Appl., 413:1 (2006), 155–176  crossref  mathscinet  zmath  isi  elib  scopus
    14. Müller M., “Convex trace functions on quantum channels and the additivity conjecture”, Phys. Rev. A, 79:5 (2009), 052332, 9 pp.  crossref  adsnasa  isi  elib  scopus
    15. Audenaert K.M.R., “A note on the $p\to q$ norms of 2-positive maps”, Linear Algebra Appl., 430:4 (2009), 1436–1440  crossref  mathscinet  zmath  isi  elib  scopus
    16. Montanaro A., “Weak Multiplicativity for Random Quantum Channels”, Commun. Math. Phys., 319:2 (2013), 535–555  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    17. Fukuda M., Gour G., “Additive Bounds of Minimum Output Entropies for Unital Channels and an Exact Qubit Formula”, IEEE Trans. Inf. Theory, 63:3 (2017), 1818–1828  crossref  mathscinet  zmath  isi  scopus
    18. Filippov S.N., Magadov K.Yu., Jivulescu M.A., “Absolutely Separating Quantum Maps and Channels”, New J. Phys., 19 (2017), 083010  crossref  mathscinet  isi  scopus
    19. Sergeev I., “Generalizations of 2-Dimensional Diagonal Quantum Channels With Constant Frobenius Norm”, Rep. Math. Phys., 83:3 (2019), 349–372  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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