Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture

Abstract

I show that if a finite-dimensional density matrix has strictly smaller von Neumann entropy than a second one of the same dimension (and the rank is not bigger), then sufficiently (but finitely) many tensor-copies of the first density matrix majorize a density matrix whose single-body marginals are all exactly equal to the second density matrix. This implies an affirmative solution of the exact catalytic entropy conjecture (CEC) introduced by Boes et al. [PRL 122, 210402 (2019)]. Both the Lemma and the solution to the CEC transfer to the classical setting of finite-dimensional probability vectors (with permutations of entries instead of unitary transformations for the CEC).

v2: ~3.5 + 1 pages; Improved presentation, additional appendix; final version for publication in Quantum

References in corpus (1)

• Multiple-copy entanglement transformation and entanglement catalysis

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