Quantum Fisher Information as the Convex Roof of Variance

2013/02/21 by Sixia Yu, Yu, Sixia · 8 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #quant-ph

paper · pdf · doi:10.48550/arxiv.1302.5311

2 Pages

arxiv created 2013/02/21 · arxiv updated 2013/02/22

Abstract

Quantum Fisher information places the fundamental limit to the accuracy of estimating an unknown parameter. Here we shall provide the quantum Fisher information an operational meaning: a mixed state can be so prepared that a given observable has the minimal averaged variance, which equals exactly to the quantum Fisher information for estimating an unknown parameter generated by the unitary dynamics with the given observable as Hamiltonian. In particular we shall prove that the quantum Fisher information is the convex roof of the variance, as conjectured by Toth and Petz based on numerical and analytical evidences, by constructing explicitly a pure-state ensemble of the given mixed state in which the averaged variance of a given observable equals to the quantum Fisher information.

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