Covariance and Fisher information in quantum mechanics

By Dénes Petz. 2001

138 citations recorded by the source corpus.

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 emphasize that Fisher information is 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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/71457e999ec956989e336d660259b96ccac92bd8

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Quantum metrology with nonclassical states of atomic ensembles (2016, background): “In this case the quantum Fisher information never increases (Fujiwara, 2001; Petz, 2002): FQ [ Λ(ρ̂θ) ] ≤ FQ [ ρ̂θ ] .”
Introduction to Quantum Fisher Information (2010, background): “The paper [43] is followed here.”