Asymptotic majorization of finite probability distributions

Abstract

This paper studies majorization of high tensor powers of finitely supported probability distributions. Viewing probability distributions as a resource with majorization as a means of transformation corresponds to the resource theory of pure bipartite quantum states under LOCC transformations vis-\`a-vis Nielsen's Theorem. In [T. Fritz (2017)] a formula for the asymptotic exchange rate between any two finitely supported probability distributions was conjectured. The main result of the present paper is Theorem 3.11, which resolves this conjecture.