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Quantum $f$ $f$ -divergences via Nussbaum–Szkoła distributions and applications to $f$ $f$ -divergence inequalities

George Androulakis

Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA

E-mail Address: giorgis@math.sc.edu

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and

Tiju Cherian John

Wyant College of Optical Sciences, The University of Arizona, Tucson, AZ 85721, USA

E-mail Address: tijucherian@fulbrightmail.org

Corresponding author.

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https://doi.org/10.1142/S0129055X23600024Cited by:3 (Source: Crossref)

This article is part of the issue:

Special Issue on Mathematical Results in Quantum Mechanics (QMath15)

Abstract

The main result in this paper shows that the quantum $f$ $f$ -divergence of two states is equal to the classical $f$ $f$ -divergence of the corresponding Nussbaum–Szkoła distributions. This provides a general framework for studying certain properties of quantum entropic quantities using the corresponding classical entities. The usefulness of the main result is illustrated by obtaining several quantum $f$ $f$ -divergence inequalities from their classical counterparts. All results presented here are valid in both finite and infinite dimensions and hence can be applied to continuous variable systems as well. A comprehensive review of the instances in the literature where Nussbaum–Szkoła distributions are used, is also provided in this paper.

In memory of K. R. Parthasarathy

Keywords:

AMSC: 81P17, 81P99

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