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

This article is cited in 43 scientific papers (total in 43 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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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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  • Теория вероятностей и ее применения Theory of Probability and its Applications
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