Despite the central importance of quantum entanglement in quantum technologies, the understanding of the optimal ways to exploit it is still beyond our reach, and even measuring entanglement in an operationally meaningful way is prohibitively difficult. Here we study two fundamental tasks in the processing of entanglement: entanglement testing, which is a quantum state discrimination problem concerned with entanglement detection in the many-copy regime, and entanglement distillation, concerned with purifying entanglement from noisy entangled states. We introduce a way of benchmarking the performance of distillation that focuses on the best achievable error rather than its yield in the asymptotic limit. When the underlying set of operations used for entanglement distillation is the axiomatic class of non-entangling operations, we show that the two figures of merit for entanglement testing and distillation coincide. We solve both problems by proving a generalised quantum Sanov's theorem, enabling the exact evaluation of asymptotic error rates of composite quantum hypothesis testing. We show in particular that the asymptotic figure of merit is given by the reverse relative entropy of entanglement, a single-letter quantity that can be evaluated using only a single copy of a quantum state -- a distinct feature among measures of entanglement that quantify the optimal performance of information-theoretic tasks.

翻译：尽管量子纠缠在量子技术中具有核心重要性，我们对其最优利用方式的理解仍遥不可及，甚至以操作上有意义的方式测量纠缠也极其困难。本文研究纠缠处理中的两个基本任务：纠缠测试（这是一个涉及多副本体系中纠缠检测的量子态区分问题）和纠缠蒸馏（涉及从含噪纠缠态中纯化纠缠）。我们引入了一种蒸馏性能的基准测试方法，其关注点在于渐近极限下可达到的最佳误差而非产率。当用于纠缠蒸馏的基础操作集是公理化的非纠缠操作类时，我们证明纠缠测试与蒸馏的两个性能指标完全一致。通过证明广义量子Sanov定理，我们解决了这两个问题，从而能够精确计算复合量子假设检验的渐近错误率。我们特别证明，该渐近性能指标由反向相对熵纠缠给出——这是一个仅需量子态的单副本即可计算的单字母量值，在量化信息论任务最优性能的纠缠度量中具有独特特征。