论文标题
典型性的相关性和确切催化熵的肯定解决方案
Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture
论文作者
论文摘要
我表明，如果有限维密度矩阵严格比相同维度的第二个（并且等级不大）的von Neumann熵较小，那么第一密度矩阵的许多张张量构成了一个密度矩阵，其单体MARGINAL的单个密度均匀等于二级密度矩阵。这意味着Boes等人引入的精确催化熵猜想（CEC）的肯定解。 [PRL 122，210402（2019）]。 CEC转移到有限维概率向量的经典设置（带有条目的排列而不是CEC的单一转换）的引理和解决方案。
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).
