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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 1, Pages 133–143 (Mi tvp151)  

This article is cited in 41 scientific papers (total in 41 papers)

Complementary channels and the additivity problem

A. S. Holevo

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We explore the complementarity between output and environment of a quantum channel (or, more generally, completely positive (CP) map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, the validity of the mutiplicativity/additivity conjecture for a class of CP maps implies its validity for complementary maps. The class of CP maps complementary to entanglement-breaking ones is described and is shown to contain diagonal CP maps as a proper subclass, resulting in a new class of CP maps (channels) for which the multiplicativity/additivity holds. Covariant and Gaussian channels are discussed briefly in this context.

Keywords: quantum channel, completely positive map, additivity conjecture.


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English version:
Theory of Probability and its Applications, 2007, 51:1, 92–100

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Document Type: Article
Received: 07.10.2005

Citation: A. S. Holevo, “Complementary channels and the additivity problem”, Teor. Veroyatnost. i Primenen., 51:1 (2006), 133–143; Theory Probab. Appl., 51:1 (2007), 92–100

Citation in format AMSBIB
\by A.~S.~Holevo
\paper Complementary channels and the additivity problem
\jour Teor. Veroyatnost. i Primenen.
\yr 2006
\vol 51
\issue 1
\pages 133--143
\jour Theory Probab. Appl.
\yr 2007
\vol 51
\issue 1
\pages 92--100

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    This publication is cited in the following articles:
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    2. A. S. Holevo, “Single-Mode Quantum Gaussian Channels: Structure and Quantum Capacity”, Problems Inform. Transmission, 43:1 (2007), 1–11  mathnet  crossref  mathscinet  isi
    3. Caruso F., Giovannetti V., “Qubit quantum channels: A characteristic function approach”, Phys. Rev. A, 76:4 (2007), 042331, 10 pp.  crossref  adsnasa  isi  elib  scopus
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    5. 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
    6. Cubitt T.S., Ruskai M.B., Smith G., “The structure of degradable quantum channels”, J. Math. Phys., 49:10 (2008), 102104, 27 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
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    19. Fischmann J., Bruzda W., Khoruzhenko B.A., Sommers H.-J., Życzkowski K., “Induced Ginibre ensemble of random matrices and quantum operations”, J. Phys. A, 45:7 (2012), 075203, 31 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
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    25. G. G. Amosov, “On estimating the output entropy of the tensor product of a phase-damping channel and an arbitrary channel”, Problems Inform. Transmission, 49:3 (2013), 224–231  mathnet  crossref  isi  elib
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    28. 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
    29. Giovannetti V., Garcia-Patron R., Cerf N.J., Holevo A.S., “Ultimate Classical Communication Rates of Quantum Optical Channels”, Nat. Photonics, 8:10 (2014), 796–800  crossref  adsnasa  isi  scopus
    30. Al Nuwairan M., “The Extreme Points of $\mathrm{SU}(2)$-Irreducibly Covariant Channels”, Int. J. Math., 25:6 (2014), 1450048  crossref  mathscinet  zmath  isi  scopus
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    34. G. G. Amosov, I. Yu. Zhdanovskii, “Structure of the Algebra Generated by a Noncommutative Operator Graph which Demonstrates the Superactivation Phenomenon for Zero-Error Capacity”, Math. Notes, 99:6 (2016), 924–927  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    35. 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
    36. Zhuang Q., Zhu E.Y., Shor P.W., “Additive Classical Capacity of Quantum Channels Assisted By Noisy Entanglement”, Phys. Rev. Lett., 118:20 (2017), 200503  crossref  mathscinet  isi  scopus
    37. Kuramochi Yu., “Quantum Incompatibility of Channels With General Outcome Operator Algebras”, J. Math. Phys., 59:4 (2018), 042203  crossref  mathscinet  zmath  isi  scopus
    38. Mukhamedov F., Watanabe N., “On S-Mixing Entropy of Quantum Channels”, Quantum Inf. Process., 17:6 (2018), UNSP 148  crossref  mathscinet  isi  scopus
    39. 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
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  • Теория вероятностей и ее применения Theory of Probability and its Applications
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