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

• URL: http://arxiv.org/abs/2308.02929v1
• Date: Sat, 5 Aug 2023 18:03:13 GMT
• Title: Quantum $f$-divergences via Nussbaum-Szko{\l}a Distributions and Applications to $f$-divergence Inequalities
• Authors: George Androulakis, Tiju Cherian John
• Abstract summary: This article shows that the quantum $f$-divergence of two states is equal to the classical $f$-divergence of the corresponding Nussbaum-Szkola distributions. The usefulness of the main result is illustrated by obtaining several quantum $f$-divergence inequalities from their classical counterparts.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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