Asymptotic majorization of finite probability distributions

TL;DR

This paper proves a conjecture about the asymptotic behavior of the majorization relation between high tensor powers of finite probability distributions, linking classical resource theory and quantum state transformations.

Contribution

It resolves a conjecture on the asymptotic exchange rate between probability distributions, advancing the understanding of resource transformations in quantum information theory.

Findings

Proves the conjectured formula for asymptotic exchange rate

Establishes a connection between classical majorization and quantum state transformations

Advances the theoretical framework of resource theory in quantum information

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.