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TRANSFORMATIONS ON DENSITY OPERATORS PRESERVING GENERALISED ENTROPY OF A CONVEX COMBINATION

Part of: Basic linear algebra

Published online by Cambridge University Press:  03 May 2018

MARCELL GAÁL  and
GERGŐ NAGY
MARCELL GAÁL*
Affiliation:
Functional Analysis Research Group, University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1, Hungary email marcell.gaal.91@gmail.com
GERGŐ NAGY
Affiliation:
Institute of Mathematics, University of Debrecen, H-4002 Debrecen, PO Box 400, Hungary email nagyg@science.unideb.hu
*
✉marcell.gaal.91@gmail.com
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Abstract

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We aim to characterise those transformations on the set of density operators (which are the mathematical representatives of the states in quantum information theory) that preserve a so-called generalised entropy of one fixed convex combination of operators. The characterisation strengthens a recent result of Karder and Petek where the preservation of the same quantity was assumed for all convex combinations.

Keywords

entropydensity operatorsquantum statespreserversconvex combination

MSC classification

Primary: 15A86: Linear preserver problems
Secondary: 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 102 - 108
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This work was supported by the National Research, Development and Innovation Office NKFIH Reg. No. K-115383.

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