Convexity of quantum χ2-divergence

Frank Hansen

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


The general quantum χ2-divergence has recently been introduced by Temme et al. [Temme K, Kastoryano M, Ruskai M, Wolf M, Verstrate F (2010) J Math Phys 51:122201] and applied to quantum channels (quantum Markov processes). The quantum χ2-divergence is not unique, as opposed to the classical χ2-divergence, but depends on the choice of quantum statistics. It was noticed that the elements in a particular one-parameter family χα2(ρ,σ) of quantum χ2-divergences are convex functions in the density matrices (ρ,σ), thus mirroring the convexity of the classical χ2(p,q)-divergence in probability distributions (p,q). We prove that any quantum χ2-divergence is a convex function in its two arguments.

Original languageEnglish
Pages (from-to)10078-10080
Number of pages3
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number25
Publication statusPublished - 2011 Jun 21


  • Monotone metric
  • Operator monotone function
  • Quantum mechanics

ASJC Scopus subject areas

  • General


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