2025/07/10 by Frits Verhagen, Marco Tomamichel, Verhagen, Frits +3 · 1 citation
Physics and Astronomy · #Expression (computer science) #Generalized relative entropy #Homomorphism #Interpretation (philosophy) #Kullback–Leibler divergence #Majorization #Measure (data warehouse) #Monotone polygon #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #State (computer science) #Statistical Mechanics and Entropy
paper · pdf · doi:10.1007/s00220-026-05675-5
published in Communications in Mathematical Physics 407(7) (Springer Science+Business Media)
openalex publication_date 2026/07/01 · openalex created_date 2026/07/08 · openalex updated_date 2026/07/23
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.