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arXiv · 2601.10395

A Collection of Pinsker-type Inequalities for Quantum Divergences

Kläre Wienecke·Gereon Koßmann·René Schwonnek
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Abstract

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 $\chi^2$-divergences as well as R\'enyi 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.

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Kläre Wienecke, Gereon Koßmann, René Schwonnek. 2026-01-15. A Collection of Pinsker-type Inequalities for Quantum Divergences. https://arxiv.org/abs/2601.10395

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