Maps on positive definite operators preserving the quantum χα2 -divergence

Hong Yi Chen, György Pál Gehér, Chih Neng Liu, L. Molnár, Dániel Virosztek, Ngai Ching Wong

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum χα2-divergence for some α∈ [ 0 , 1 ]. We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.

Original languageEnglish
Pages (from-to)2267-2290
Number of pages24
JournalLetters in Mathematical Physics
Volume107
Issue number12
DOIs
Publication statusPublished - Dec 1 2017

Fingerprint

Positive definite
preserving
Divergence
divergence
operators
Cone
Operator
cones
Density Operator
Positive semidefinite
Bijective
Hilbert space

Keywords

  • Positive definite operators
  • Preservers
  • Quantum χ -divergence

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Maps on positive definite operators preserving the quantum χα2 -divergence. / Chen, Hong Yi; Gehér, György Pál; Liu, Chih Neng; Molnár, L.; Virosztek, Dániel; Wong, Ngai Ching.

In: Letters in Mathematical Physics, Vol. 107, No. 12, 01.12.2017, p. 2267-2290.

Research output: Contribution to journalArticle

Chen, Hong Yi ; Gehér, György Pál ; Liu, Chih Neng ; Molnár, L. ; Virosztek, Dániel ; Wong, Ngai Ching. / Maps on positive definite operators preserving the quantum χα2 -divergence. In: Letters in Mathematical Physics. 2017 ; Vol. 107, No. 12. pp. 2267-2290.
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