论文标题
基于端口的传送的相当好测量的最佳性
Optimality of the pretty good measurement for port-based teleportation
论文作者
论文摘要
基于端口的传送（PBT）是一种协议，在该协议中，Alice使用在共享纠缠的多部分状态上测量端口状态和向前的经典通信，将未知的量子状态传送到BOB。在本文中，我们给出了一个明确的证据，即所谓的相当良好的测量或平方根测量对于PBT协议是最佳的，具有最大纠缠状态为端口状态的独立副本。然后，我们证明，即使优化端口状态以产生最佳的PBT协议，同一测量仍然是最佳的。因此，在两种情况下，都有一个特别好的测量值，可以达到最佳性能。以下众所周知的事实是这些结果证明的关键要素：（i）PBT的自然对称性，导致对表示理论数据的描述； （ii）PBT与某些州歧视问题的运营等效性，这使我们能够采用相关半决赛计划的双重性。一路上，我们在[Studziński等人，2017]和[Mozrzymas等，2018]中仅使用来自单位和对称组的表示理论的标准技术，在[Studziński等，2017]和[Mozrzymas等人，2018]中重新阐明了对PBT协议性能的表达理论公式。提供这些美丽的公式的简化推导是本文的主要目标之一。
Port-based teleportation (PBT) is a protocol in which Alice teleports an unknown quantum state to Bob using measurements on a shared entangled multipartite state called the port state and forward classical communication. In this paper, we give an explicit proof that the so-called pretty good measurement, or square-root measurement, is optimal for the PBT protocol with independent copies of maximally entangled states as the port state. We then show that the very same measurement remains optimal even when the port state is optimized to yield the best possible PBT protocol. Hence, there is one particular pretty good measurement achieving the optimal performance in both cases. The following well-known facts are key ingredients in the proofs of these results: (i) the natural symmetries of PBT, leading to a description in terms of representation-theoretic data; (ii) the operational equivalence of PBT with certain state discrimination problems, which allows us to employ duality of the associated semidefinite programs. Along the way, we rederive the representation-theoretic formulas for the performance of PBT protocols proved in [Studziński et al., 2017] and [Mozrzymas et al., 2018] using only standard techniques from the representation theory of the unitary and symmetric groups. Providing a simplified derivation of these beautiful formulas is one of the main goals of this paper.
