Isometries and relative entropy preserving maps on density operators

Lajos Molnár, Gergo Nagy

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this article we consider certain kinds of metrics and relative entropies on sets of density operators acting on a finite-dimensional complex Hilbert space. The metrics are the ones induced by the von Neumann-Schatten p-norms. We describe the general form of 'a priori' nonsurjective isometries of the space of all density operators with respect to those distances. In the second part of this article we study mappings preserving entropic quantities. We determine the structure of 'a priori' nonsurjective maps on the set of all density operators which leave a certain measure of relative entropy invariant and also characterize the surjective maps on the set of all invertible density operators with similar invariance properties.

Original languageEnglish
Pages (from-to)93-108
Number of pages16
JournalLinear and Multilinear Algebra
Volume60
Issue number1
DOIs
Publication statusPublished - Jan 1 2012

Keywords

  • density operators
  • isometries
  • p-norms
  • preservers
  • relative entropies

ASJC Scopus subject areas

  • Algebra and Number Theory

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