Geodesic
Algebraic methods of the study of quantum information transfer channels
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum computing, Tome 138 (2017), pp. 3-10.

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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, minimal output entropy, noncommutative operator graph, quantum channel capacity with zero error.
Mots-clés : Kraus decomposition 
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     author = {G. G. Amosov},
     title = {Algebraic methods of the study of quantum information transfer channels},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {138},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_138_a0/}
}
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G. G. Amosov. Algebraic methods of the study of quantum information transfer channels. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum computing, Tome 138 (2017), pp. 3-10. http://geodesic.mathdoc.fr/item/INTO_2017_138_a0/