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Singular Value Decomposition And Matrix Reorderings In Quantum Information Theory

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  • JAROSŁAW ADAM MISZCZAK

    (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 theMathematicacomputing system implementing basic functions used in the calculations related to quantum information theory.

Suggested Citation

  • Jarosław Adam Miszczak, 2011. "Singular Value Decomposition And Matrix Reorderings In Quantum Information Theory," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(09), pages 897-918.
    • Handle: RePEc:wsi:ijmpcx:v:22:y:2011:i:09:n:s0129183111016683
    DOI: 10.1142/S0129183111016683
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