Characterizations of symmetric monotone metrics on the state space of quantum systems

Frank Hansen

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the characterization, initiated by Morozova, Chentsov and Petz, of these metrics by providing a closed and tractable formula for the set of Morozova-Chentsov functions. In addition, we provide a continuously increasing bridge between the smallest and largest symmetric monotone metrics.

Original languageEnglish
Pages (from-to)597-605
Number of pages9
JournalQuantum Information and Computation
Issue number7
Publication statusPublished - 2006 Nov
Externally publishedYes


  • Monotone metrics
  • Quantum fisher information

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Computational Theory and Mathematics


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