Introduction to Quantum Fisher Information

By Dénes Petz, Catalin Ghinea. 2010

186 citations recorded by the source corpus.

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.

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

View Paper: https://www.semanticscholar.org/paper/3457487eb4de64945b39428d59254cbf4e6478d0

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In Artificial Intelligence

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Citations in the corpus

The χ2-divergence and mixing times of quantum Markov processes (2010, background): “He furthermore was able to relate several generalized relative entropies (which he deﬁned much earlier [13] and referred to as quasi-entropies) to monotone Riemannian metrics [15–17].”
Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution (2017, background): “The QFIM depends only on the following quantities w ≡ 〈Ψ±|Ψ∓〉= 〈Ψ|exp(isP)|Ψ〉 , p2 ≡ 〈Ψ±”
Quantum metrology with nonclassical states of atomic ensembles (2016, background): “In this case the quantum Fisher information never increases (Petz, 1996; Petz and Ghinea, 2011):”
Quantum Fisher information matrix and multiparameter estimation (2019, background): “also wrote a thorough technical introduction on QFI [17].”