Affiliation:
1. Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland
Abstract
We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyze the correspondence between quantum states and operations with the help of Jamiołkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations, we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.
Publisher
World Scientific Pub Co Pte Lt
Subject
Computational Theory and Mathematics,Computer Science Applications,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
40 articles.
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