A characterization of extended monotone metrics
It is well-known that information geometry was initiated by S. Amari. In classical information geometry, the Fisher metric is characterized as Riemannian metric on the probability simplex. In quantum information geometry, D.Petz gave the monotone metric (quantum Fisher information) on quantum state space. In the present paper, the author gives the extension of Petz's result. That is, the characterization of the extended monotone metric on the set of all positive Hermitian matrices is given, as L. L. Campbell gave an extension of the characterization from probability simplex to positive cone in classical case.
scientific article; zbMATH DE number 5821961