Order automorphisms on positive definite operators and a few applications

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We first determine the order automorphisms of the set of all positive definite operators with respect to the usual order and to the so-called chaotic order. We then apply those results to the following problems: (1) description of all bijective transformations on the space of nonsingular density operators (quantum states) which preserve the Umegaki or the Belavkin-Staszewski relative entropy; (2) characterization of the logarithmic product as the essentially unique binary operation on the set of positive definite operators that makes it an ordered commutative group with respect to the chaotic order.

Original languageEnglish
Pages (from-to)2158-2169
Number of pages12
JournalLinear Algebra and Its Applications
Volume434
Issue number10
DOIs
Publication statusPublished - May 15 2011

Fingerprint

Positive definite
Automorphisms
Entropy
Operator
Density Operator
Binary operation
Relative Entropy
Bijective
Quantum State
Logarithmic

Keywords

  • Chaotic order
  • Logarithmic product
  • Order
  • Order automorphisms
  • Ordered groups
  • Positive definite operators
  • Preservers
  • Quantum relative entropies

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Numerical Analysis

Cite this

Order automorphisms on positive definite operators and a few applications. / Molnár, L.

In: Linear Algebra and Its Applications, Vol. 434, No. 10, 15.05.2011, p. 2158-2169.

Research output: Contribution to journalArticle

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