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Advances in Mathematical Physics

Preservers for the Tsallis Entropy of Convex Combinations of Density Operators

Xiaochun Fang, Yihui Lao

Published Jun 4, 2018• 3 citations
Publisher

Abstract

Let H be a complex separable Hilbert space; we first characterize the unitary equivalence of two density operators by use of Tsallis entropy and then obtain the form of a surjective map on density operators preserving Tsallis entropy of convex combinations.
DOI
10.1155/2018/5296085

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Abstract 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 ppp -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∗C^{\ast }C∗ -algebra.
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