论文标题
最小的可计算纠缠单调
A smallest computable entanglement monotone
论文作者
论文摘要
降雨相对熵的量子状态是其可蒸馏的纠缠最紧的上限 - 它具有清晰的物理解释，将纠缠作为一种资源，并且可以通过凸面编程有效地计算。众所周知，它本身就是一个选择性的单调。在这项工作中，我们通过表明它在选择性操作的作用下是单调的，从而加强了对降雨相对熵的解释，从而完全保留了部分转置的阳性，并合理地量化了纠缠。也就是说，我们证明，这种操作产生的合奏的相对熵不会超过预期中初始状态的降雨相对熵，从而产生最小，最保守的可计算选择性选择性纠缠单调。此外，我们表明，这不仅对于原始的降雨相对熵是正确的，而且对于从各种rényi相对熵得出的降雨相对熵也是如此。作为这些发现的应用，我们证明在非反应和渐近设置中，概率近似近似的纠缠状态是由各种降雨相对熵从上面界定的。
The Rains relative entropy of a bipartite quantum state is the tightest known upper bound on its distillable entanglement -- which has a crisp physical interpretation of entanglement as a resource -- and it is efficiently computable by convex programming. It has not been known to be a selective entanglement monotone in its own right. In this work, we strengthen the interpretation of the Rains relative entropy by showing that it is monotone under the action of selective operations that completely preserve the positivity of the partial transpose, reasonably quantifying entanglement. That is, we prove that Rains relative entropy of an ensemble generated by such an operation does not exceed the Rains relative entropy of the initial state in expectation, giving rise to the smallest, most conservative known computable selective entanglement monotone. Additionally, we show that this is true not only for the original Rains relative entropy, but also for Rains relative entropies derived from various Rényi relative entropies. As an application of these findings, we prove, in both the non-asymptotic and asymptotic settings, that the probabilistic approximate distillable entanglement of a state is bounded from above by various Rains relative entropies.
