A Collection of Pinsker-type Inequalities for Quantum Divergences

Fuente: arXiv
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Main Authors: Wienecke, Kläre, Koßmann, Gereon, Schwonnek, René
Format: Preprint
Published: 2026
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author Wienecke, Kläre
Koßmann, Gereon
Schwonnek, René
author_facet Wienecke, Kläre
Koßmann, Gereon
Schwonnek, René
contents Pinsker's inequality sets a lower bound on the Umegaki divergence of two quantum states in terms of their trace distance. In this work, we formulate corresponding estimates for a variety of quantum and classical divergences including $f$-divergences like Hellinger and $χ^2$-divergences as well as Rényi divergences and special cases thereof like the Umegaki divergence, collision divergence, max divergence. We further provide a strategy on how to adapt these bounds to smoothed divergences.
format Preprint
id arxiv_https___arxiv_org_abs_2601_10395
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Collection of Pinsker-type Inequalities for Quantum Divergences
Wienecke, Kläre
Koßmann, Gereon
Schwonnek, René
Quantum Physics
Pinsker's inequality sets a lower bound on the Umegaki divergence of two quantum states in terms of their trace distance. In this work, we formulate corresponding estimates for a variety of quantum and classical divergences including $f$-divergences like Hellinger and $χ^2$-divergences as well as Rényi divergences and special cases thereof like the Umegaki divergence, collision divergence, max divergence. We further provide a strategy on how to adapt these bounds to smoothed divergences.
title A Collection of Pinsker-type Inequalities for Quantum Divergences
topic Quantum Physics
url https://arxiv.org/abs/2601.10395