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Algebraic Methods of the Study of Quantum Information Transfer Channels

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Abstract

Kraus representation of quantum information transfer channels is widely used in practice. We present examples of Kraus decompositions for channels that possess the covariance property with respect to the maximal commutative group of unitary operators. We show that in some problems (for example, the problem on the estimate of the minimal output entropy of the channel), the choice of a Kraus representation with nonminimal number of Kraus operators is relevant. We also present certain algebraic properties of noncommutative operator graphs generated by Kraus operators for the case of quantum channels that demonstrate the superactivation phenomenon.

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Authors and Affiliations

  1. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

    G. G. Amosov

  2. Saint Petersburg State University, Saint Petersburg, Russia

    G. G. Amosov

  3. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    G. G. Amosov

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  1. G. G. Amosov
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Correspondence to G. G. Amosov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 138, Quantum Computing, 2017.

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Amosov, G.G. Algebraic Methods of the Study of Quantum Information Transfer Channels. J Math Sci 241, 109–116 (2019). https://doi.org/10.1007/s10958-019-04411-w

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  • DOI: https://doi.org/10.1007/s10958-019-04411-w

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