Entanglement purification is an indispensable ingredient in extended quantum communication networks and usually determines the efficiency and communication rate of quantum communication protocols. Different from all existing entanglement purification protocols (EPPs) where two or more copies of low quality mixed entangled states are selected from the same ensemble, here we describe a general and optimal EPP for arbitrary initial mixed states from different ensembles. We show that the successful operation of EPP may not obtain a higher fidelity mixed state, while the discarded source pair, which is usually regarded as a failure in existing EPPs, may have residual entanglement and can be reused to increase the yield of entanglement purification. We give the criterions of both the successful purification to obtain a higher fidelity mixed state and the existence of residual entanglement. Moreover, we reveal that entanglement purification procedure causes some entanglement loss. Finally, we provide an optimal approach to reduce the entanglement loss. This approach can also be used to increase the yield of entanglement purification. Our EPP may have potential application in long-distance quantum communications.

中文翻译：

---

纯化残留缠结。

纠缠纯化是扩展的量子通信网络中必不可少的成分，通常决定着量子通信协议的效率和通信速率。与所有现有的纠缠纯化协议（EPP）不同，在该协议中，从同一集合中选择了两个或多个低质量的混合纠缠态副本，在此我们描述了来自不同集合的任意初始混合态的通用和最佳EPP。我们表明，EPP的成功运行可能无法获得更高保真度的混合状态，而通常被视为现有EPP中的故障的废弃源对可能具有残留纠缠，可以重新使用以提高纠缠提纯的产量。我们给出了成功纯化以获得更高保真度混合状态的标准以及存在残留纠缠的标准。此外，我们揭示了纠缠纯化过程会导致一些纠缠损失。最后，我们提供了一种减少缠结损失的最佳方法。该方法也可以用于增加纠缠纯化的产率。我们的EPP可能在长距离量子通信中具有潜在的应用。