Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of α-z Relative Entropies

• URL: http://arxiv.org/abs/2507.07520v2
• Date: Tue, 09 Sep 2025 15:05:35 GMT
• Title: Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of α-z Relative Entropies
• Authors: Frits Verhagen, Marco Tomamichel, Erkka Haapasalo,
• Abstract summary: We offer the first operational interpretation of the alpha-z relative entropies, a measure of distinguishability between two quantum states.<n>We show that such transformations exist if and only if all the alpha-z relative entropies of the two pairs are ordered.
• Score: 11.151457846264185
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We offer the first operational interpretation of the {\alpha}-z relative entropies, a measure of distinguishability between two quantum states introduced by Jak\v{s}i\'c 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 {\alpha}-z relative entropies of the two pairs are ordered. In this setting, the {\alpha} 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.

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