Asymptotic majorization of finite probability distributions

Asger Kj{\ae}rulff Jensen

Asymptotic majorization of finite probability distributions

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arxiv 1808.05157 v1 pith:JBD7JUIO submitted 2018-08-15 quant-ph cs.ITmath.IT

Asger Kj{ae}rulff Jensen This is my paper · ORCID

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keywords distributionsprobabilitymajorizationasymptoticfinitelyresourcesupportedtheorem

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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.

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Error exponents for tripartite-to-bipartite entanglement transformations
quant-ph 2025-07 accept novelty 7.0 of 10

For pure tripartite states, the optimal deterministic rate is the minimum of two min-entropies of entanglement, and the direct and strong converse error exponents are given by explicit rate formulas.

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