Geometrical Statistics--Classical and Quantum

Details Geometrical Statistics--Classical and Quantum Geometrical Statistics--Classical and Quantum

2005-09-02

arxiv.org/abs/quant-ph/0509017v1

Physics

Quantum Physics

Talk at the third Vaxjo conference on Quantum Theory: Reconsideration of foundations

Scientific paper

This is a review of the ideas behind the Fisher--Rao metric on classical probability distributions, and how they generalize to metrics on density matrices. As is well known, the unique Fisher--Rao metric then becomes a large family of monotone metrics. Finally I focus on the Bures--Uhlmann metric, and discuss a recent result that connects the geometric operator mean to a geodesic billiard on the set of density matrices.

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