Abstract
July 5 - 14.30-15.30
D.Petz
- Covariance and Fisher information in quantum mechanics
Variance and Fisher information are ingredients of the Cramer-Rao
inequality. We regard Fisher information as a Riemannian metric on a
quantum statistical manifold and choose monotonicity under coarse graining
as the fundamental property of variance and Fisher information. In this
approach we show that there is a kind of dual one-to-one correspondence
between the candidates of the two concepts. We emphasis that Fisher
informations are obtained from relative entropies as contrast functions on
the state space and argue that the scalar curvature might be interpreted
as an uncertainty density
on a statistical manifold.
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