Many applications of the emerging quantum technologies, such as quantum teleportation and quantum key distribution, require singlets, maximally entangled states of two quantum bits. It is thus of utmost importance to develop optimal procedures for establishing singlets between remote parties. As has been shown very recently, singlets can be obtained from other quantum states by using a quantum catalyst, an entangled quantum system which is not changed in the procedure. In this work we take this idea further, investigating properties of entanglement catalysis and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst, which can enable all possible transformations in this setup. We demonstrate the advantage of catalysis in asymptotic settings, going beyond the typical assumption of independent and identically distributed systems. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel when assisted by entangled catalysts. For various types of quantum channels our results lead to optimal protocols, allowing to establish the maximal number of singlets with a single use of the channel.

中文翻译：

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量子态和噪声通道的纠缠催化

新兴量子技术的许多应用，例如量子隐形传态和量子密钥分发，都需要单态，即两个量子比特的最大纠缠态。因此，制定在远程各方之间建立单线的最佳程序至关重要。正如最近所表明的，通过使用量子催化剂，可以从其他量子态获得单态，这是一种在过程中不改变的纠缠量子系统。在这项工作中，我们进一步深化了这一想法，研究了纠缠催化的性质及其在量子通信中的作用。对于二分纯态之间的转换，我们证明了通用催化剂的存在，它可以实现该设置中所有可能的转换。我们证明了渐近设置中催化的优势，超越了独立同分布系统的典型假设。我们进一步开发了估计单线态数量的方法，这些单线态在纠缠催化剂的辅助下可以通过噪声量子通道建立。对于各种类型的量子通道，我们的结果得出最佳协议，允许通过单次使用通道建立最大数量的单峰。