Maps on positive definite operators preserving the quantum χα2 -divergence

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

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2 Citations (Scopus)


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
Issue number12
Publication statusPublished - Dec 1 2017



  • Positive definite operators
  • Preservers
  • Quantum χ -divergence

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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