- 95-259 Denes PETZ, Csaba SUDAR
- Geometries of Quantum States
Jun 6, 95
(auto. generated ps),
of related papers
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