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Maps on Quantum States in $C^{\ast }$-algebras Preserving von Neumann Entropy or Schatten $p$-norm of Convex Combinations

Part of: Special classes of linear operators

Published online by Cambridge University Press:  09 January 2019

Marcell Gaál
Marcell Gaál*
Affiliation:
Functional Analysis Research Group, University of Szeged, H-6720 Szeged, Hungary Email: marcell.gaal.91@gmail.com
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Abstract

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Very recently, Karder and Petek completely described maps on density matrices (positive semidefinite matrices with unit trace) preserving certain entropy-like convex functionals of any convex combination. As a result, maps could be characterized that preserve von Neumann entropy or Schatten $p$-norm of any convex combination of quantum states (whose mathematical representatives are the density matrices). In this note we consider these latter two problems on the set of invertible density operators, in a much more general setting, on the set of positive invertible elements with unit trace in a $C^{\ast }$-algebra.

Keywords

density operatorentropySchatten p-normC∗ -algebranormalized tracepreserver

MSC classification

Primary: 47B49: Transformers, preservers (operators on spaces of operators)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 1 , March 2019 , pp. 75 - 80
Copyright
© Canadian Mathematical Society 2018 

Footnotes

This work was partially supported by the Hungarian National Research, Development and Innovation Office – NKFIH Reg.No. K115383.

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