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

Details Characterization of symmetric monotone metrics on the state space of quantum systems Characterization of symmetric monotone metrics on the state space of quantum systems

2006-01-26

arxiv.org/abs/math-ph/0601056v3

Quantum Information and Computation 6 (2006) 597-605

Physics

Mathematical Physics

Minor revision with new title and abstract as suggested by a referee

Scientific paper

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.

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