Geometries of quantum states

Dénes Petz, Csaba Sudár

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137 Citations (Scopus)


The quantum analog of the Fisher information metric of a probability simplex is searched and several Riemannian metrics on the set of positive definite density matrices are studied. Some of them appeared in the literature in connection with Cramér-Rao-type inequalities or the generalization of the Berry phase to mixed states. They are shown to be stochastically monotone here. All stochastically monotone Riemannian metrics are characterized by means of operator monotone functions and it is proven that there exist a maximal and a minimal among them. A class of metrics can be extended to pure states and a constant multiple of the Fubini-Study metric appears in the extension.

Original languageEnglish
Pages (from-to)2662-2673
Number of pages12
JournalJournal of Mathematical Physics
Issue number6
Publication statusPublished - Jun 1 1996


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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