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arxiv: 1008.2417 · v1 · pith:YTVAR2C7 · submitted 2010-08-14 · quant-ph

Introduction to quantum Fisher information

Denes Petz , Catalin Ghinea This is my paper

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The subject of this paper is a mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory. If the monotonicity is the main requirement, then there are several quantum versions parametrized by a function. In physical applications the minimal is the most popular. There is a one-to-one correspondence between Fisher informations (called also monotone metrics) and abstract covariances. The skew information and the chi-square-divergence are treated here as particular cases.

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  1. Bayesian Monotone Metrics for Multiparameter Quantum Estimation

    quant-ph 2026-07 unverdicted novelty 7.0

    Bayesian monotone metrics extend Petz metrics to prior-averaged states, yielding computable lower bounds on multiparameter Bayes risk that dominate van Trees bounds and can be optimized via a one-parameter subfamily.