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Quantum statistical information contained in a semi-classical Fisher--Husimi measure

F. Pennini·A. Plastino·G. L. Ferri
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Abstract

We study here the difference between quantum statistical treatments and semi-classical ones, using as the main research tool a semi-classical, shift-invariant Fisher information measure built up with Husimi distributions. Its semi-classical character notwithstanding, this measure also contains information of a purely quantal nature. Such a tool allows us to refine the celebrated Lieb bound for Wehrl entropies and to discover thermodynamic-like relations that involve the degree of delocalization. Fisher-related thermal uncertainty relations are developed and the degree of purity of canonical distributions, regarded as mixed states, is connected to this Fisher measure as well.

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F. Pennini, A. Plastino, G. L. Ferri. 2005-09-18. Quantum statistical information contained in a semi-classical Fisher--Husimi measure. https://doi.org/10.1016/j.physleta.2006.06.003

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