95-259 Denes PETZ, Csaba SUDAR
Geometries of Quantum States (42K, TeX) Jun 6, 95
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Abstract. The quantum analogue 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 Cramer-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 the Fubini-Study metric shows up there.

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