Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states. First, we define the unextendible entanglement, a family of entanglement measures based on the concept of a state-dependent set of free states. The intuition behind these measures is that the more entangled a bipartite state is, the less entangled each of its individual systems is with a third party. Second, we demonstrate that the unextendible entanglement is an entanglement monotone under two-extendible quantum operations, including local operations and one-way classical communication as a special case. Normalization and faithfulness are two other desirable properties of unextendible entanglement, which we establish here. We further show that the unextendible entanglement provides efficiently computable benchmarks for the rate of exact entanglement or secret key distillation, as well as the overhead of probabilistic entanglement or secret key distillation.

翻译：纠缠是量子力学的重要特征，其具有称为不可扩展性的关键性质。本文提出一个用于量化和研究一般双体量子态不可扩展性的理论框架。首先，我们定义不可扩展纠缠——一类基于态依赖自由态集的纠缠度量族。这些度量的直观思想是：双体量子态的纠缠程度越高，其各个子系统与第三方之间的纠缠程度就越低。其次，我们证明不可扩展纠缠在双可扩展量子操作（包括局域操作和单向经典通信作为特例）下是纠缠单调量。归一化性和忠实性是不可扩展纠缠另外两个理想性质，本文对此进行了确立。我们进一步证明，不可扩展纠缠可为精确纠缠或密钥蒸馏的速率以及概率性纠缠或密钥蒸馏的代价提供可高效计算的基准。