01014nas a2200157   4500000000100000000000100001000000100002008004100003260000600044100002200050245008600072300001400158490000700172520066300179022001400842       2011                            d  c91 aJaroslaw Miszczak00aSingular value decomposition and matrix reorderings in quantum information theory  a897–9180 v223 aWe 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.  a0129-1831