We analytically obtain the maximum probability of converting a finite number of copies of an arbitrary two-qubit pure state to a single copy of a maximally entangled two-qubit pure state via entanglement-assisted local operations and classical communications using a two-qubit catalyst state, which may be destroyed when the conversion fails. We show that the optimal catalyst for this transformation is always more entangled than the initial state but any two-qubit state can act as a (non-optimal) catalyst. Interestingly, the entanglement of the optimal two-qubit catalyst state is shown to decrease with that of the initial state. The unitaries and measurements required for catalytic entanglement concentration are presented.

我们通过纠缠辅助局部操作和使用双量子位催化剂状态的经典通信，分析地获得了将任意双量子位纯态的有限数量副本转换为最大纠缠双量子位纯态的单个副本的最大概率，转换失败时可能会被销毁。我们表明，这种转变的最佳催化剂总是比初始状态更纠缠，但任何双量子位状态都可以充当（非最佳）催化剂。有趣的是，最佳双量子位催化剂状态的纠缠显示出随着初始状态的纠缠而减少。介绍了催化缠结浓度所需的幺正和测量。