Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $α$-z Relative Entropies
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910159777824768 |
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| author | Verhagen, Frits Tomamichel, Marco Haapasalo, Erkka |
| author_facet | Verhagen, Frits Tomamichel, Marco Haapasalo, Erkka |
| contents | We offer the first operational interpretation of the $α$-z relative entropies, a measure of distinguishability between two quantum states introduced by Jakšić et al. and Audenaert and Datta. We show that these relative entropies appear when formulating conditions for large-sample or catalytic relative majorization of pairs of flat states and certain generalizations of them. Indeed, we show that such transformations exist if and only if all the $α$-z relative entropies for $α$<1 of the two pairs are ordered. In this setting, the $α$ and z parameters are truly independent from each other. These results also yield an expression for the optimal rate of converting one flat state pair into another. Our methods use real-algebraic techniques involving preordered semirings and certain monotone homomorphisms and derivations on them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07520 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $α$-z Relative Entropies Verhagen, Frits Tomamichel, Marco Haapasalo, Erkka Quantum Physics Information Theory We offer the first operational interpretation of the $α$-z relative entropies, a measure of distinguishability between two quantum states introduced by Jakšić et al. and Audenaert and Datta. We show that these relative entropies appear when formulating conditions for large-sample or catalytic relative majorization of pairs of flat states and certain generalizations of them. Indeed, we show that such transformations exist if and only if all the $α$-z relative entropies for $α$<1 of the two pairs are ordered. In this setting, the $α$ and z parameters are truly independent from each other. These results also yield an expression for the optimal rate of converting one flat state pair into another. Our methods use real-algebraic techniques involving preordered semirings and certain monotone homomorphisms and derivations on them. |
| title | Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $α$-z Relative Entropies |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2507.07520 |