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.
Asymptotic majorization of finite probability distributions
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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.
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Error exponents for tripartite-to-bipartite entanglement transformations
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.