arXiv subjects

Frits Verhagen

Publications and source records attributed to Frits Verhagen.

2 recordsLinked to original sources

arXiv2026

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

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.

quant-ph↗

arXiv2025

Matrix Majorization in Large Samples with Varying Support Restrictions

We say that a matrix $P$ with non-negative entries majorizes another such matrix $Q$ if there is a stochastic matrix $T$ such that $Q=TP$. We study matrix majorization in large samples and in the catalytic regime in the case where the columns of the matrices need not have equal support, as has been assumed in earlier works. We focus on two cases: either there are no support restrictions (except for requiring a non-empty intersection for the supports) or the final column dominates the others. Using real-algebraic methods, we identify sufficient and almost necessary conditions for majorization in large samples or when using catalytic states under these support conditions. These conditions are given in terms of multivariate divergences that generalize the Rényi divergences. We notice that varying support conditions dramatically affect the relevant set of divergences. Our results find an application in the theory of catalytic state transformation in quantum thermodynamics.

math.ST↗