Singular value decomposition and matrix reorderings in quantum information theory

Details Singular value decomposition and matrix reorderings in quantum information theory Singular value decomposition and matrix reorderings in quantum information theory

2010-11-06

arxiv.org/abs/1011.1585v2

Int. J. Mod. Phys. C, Vol. 22, No. 9 (2011), pp. 897-918

Physics

Quantum Physics

11 pages, no figures, see http://zksi.iitis.pl/wiki/projects:mathematica-qi for related software

Scientific paper

10.1142/S0129183111016683

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 analyse the correspondence between quantum states and operations with the help of Jamiolkowski 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.

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