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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 138, Pages 3–10 (Mi into210)  
Algebraic methods of the study of quantum information transfer channels

G. G. Amosovabc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Saint Petersburg State University
c Moscow Institute of Physics and Technology
Full-text PDF (195 kB)
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.
Keywords: quantum channel, Kraus decomposition, minimal output entropy, noncommutative operator graph, quantum channel capacity with zero error.
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 2, Pages 109–116
DOI: https://doi.org/10.1007/s10958-019-04411-w
Bibliographic databases:
Document Type: Article
UDC: 519.722, 519.724, 517.983
MSC: 94A17, 94A40, 47C05
Language: Russian
Citation: G. G. Amosov, “Algebraic methods of the study of quantum information transfer channels”, Quantum computing, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 3–10; Journal of Mathematical Sciences, 241:2 (2019), 109–116
Citation in format AMSBIB
\Bibitem{Amo17}
\by G.~G.~Amosov
\paper Algebraic methods of the study of quantum information transfer channels
\inbook Quantum computing
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 138
\pages 3--10
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into210}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801247}
\zmath{https://zbmath.org/?q=an:07123786}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 2
\pages 109--116
\crossref{https://doi.org/10.1007/s10958-019-04411-w}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85069916660}
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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