A Collection of Pinsker-type Inequalities for Quantum Divergences
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909991481376768 |
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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 |