From Quasi-Entropy to Various Quantum Information Quantities

  • Fumio Hiai

    Abiko, Japan
  • Dénes Petz

    Hungarian Academy, Budapest, Hungary


The subject is the applications of the use of quasi-entropy in finite dimensional spaces to many important quantities in quantum information. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the -divergence, monotone metrics, covariance and the -divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone metrics are also characterized by their joint convexity property.

Cite this article

Fumio Hiai, Dénes Petz, From Quasi-Entropy to Various Quantum Information Quantities. Publ. Res. Inst. Math. Sci. 48 (2012), no. 3, pp. 525–542

DOI 10.2977/PRIMS/79