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arXiv · 2308.02929

Quantum $f$-divergences via Nussbaum-Szko{\l}a Distributions and Applications to $f$-divergence Inequalities

George Androulakis·Tiju Cherian John
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Abstract

The main result in this article shows that the quantum $f$-divergence of two states is equal to the classical $f$-divergence of the corresponding Nussbaum-Szko{\l}a 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 $f$-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-Szko{\l}a distributions are used, is also provided in this article.

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George Androulakis, Tiju Cherian John. 2023-08-05. Quantum $f$-divergences via Nussbaum-Szko{\l}a Distributions and Applications to $f$-divergence Inequalities. https://doi.org/10.1142/s0129055x23600024

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