Singular value decomposition and matrix reorderings in quantum information theory

TytułSingular value decomposition and matrix reorderings in quantum information theory
Publication TypeJournal Article
Rok publikacji2011
AutorzyMiszczak J
JournalJ. Mod. Phys. C
Volume22
Pagination897–918
Date Published9
ISSN0129-1831
AbstractWe 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.