Bregman divergence as relative operator entropy

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15 Citations (Scopus)


The Bregman operator divergence is introduced for density matrices by differentiation of the matrix-valued function x & x log x. This quantity is compared with the relative operator entropy of Fujii and Kamei. It turns out that the trace is the usual Umegaki's relative entropy which is the only intersection of the classes of quasi-entropies and Bregman divergences.

Original languageEnglish
Pages (from-to)127-131
Number of pages5
JournalActa Mathematica Hungarica
Issue number1-2
Publication statusPublished - Jul 1 2007


  • Bregman divergence
  • F-divergence
  • Quantum relative entropy

ASJC Scopus subject areas

  • Mathematics(all)

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