Lower bounds on the quantum Fisher information based on the variance and various types of entropies

2017/01/25 by G. Tóth, Toth, Geza · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1701.07461

openalex publication_date 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., (ΔA)²-F_{\rm Q}[\varrho,A]/4. We find that it is equal to a generalized variance defined in Petz [J. Phys. A 35, 929 (2002)] and Gibilisco, Hiai, and Petz [IEEE Trans. Inf. Theory 55, 439 (2009)]. We present an upper bound on this quantity that is proportional to the linear entropy. As expected, our relation shows that for states that are close to being pure, the quantum Fisher information over four is close to the variance. We also obtain the variance and the quantum Fisher information averaged over all Hermitian operators, and examine its relation to the von Neumann entropy. Apart from the usual quantum Fisher information, we also consider the Kubo-Mori-Bogoliubov quantum Fisher information.

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