Quantum communication enables a host of applications that cannot be achieved by classical communication means, with provably secure communication as one of the prime examples. The distance that quantum communication schemes can cover via direct communication is fundamentally limited by losses on the communication channel. By means of quantum repeaters, the reach of these schemes can be extended and chains of quantum repeaters could in principle cover arbitrarily long distances. In this work, we provide two efficient algorithms for determining the generation time and fidelity of the first generated entangled pair between the end nodes of a quantum repeater chain. The runtime of the algorithms increases polynomially with the number of segments of the chain, which improves upon the exponential runtime of existing algorithms. Our first algorithm is probabilistic and can analyze refined versions of repeater chain protocols which include intermediate entanglement distillation. Our second algorithm computes the waiting time distribution up to a pre-specified truncation time, has faster runtime than the first one and is moreover exact up to machine precision. Using our proof-of-principle implementation, we are able to analyze repeater chains of thousands of segments for some parameter regimes. The algorithms thus serve as useful tools for the analysis of large quantum repeater chain protocols and topologies of the future quantum internet.

中文翻译：

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量子中继器链中等待时间和保真度的高效计算


量子通信实现了许多传统通信方式无法实现的应用，可证明安全的通信就是最好的例子之一。量子通信方案通过直接通信所能覆盖的距离从根本上受到通信信道损耗的限制。通过量子中继器，这些方案的覆盖范围可以扩展，并且量子中继器链原则上可以覆盖任意长的距离。在这项工作中，我们提供了两种有效的算法来确定量子中继器链末端节点之间第一个生成的纠缠对的生成时间和保真度。算法的运行时间随着链段的数量呈多项式增加，这改进了现有算法的指数运行时间。我们的第一个算法是概率性的，可以分析中继器链协议的精炼版本，其中包括中间纠缠蒸馏。我们的第二个算法计算等待时间分布直至预先指定的截断时间，比第一个算法具有更快的运行时间，而且精确到机器精度。使用我们的原理验证实现，我们能够分析某些参数机制的数千个段的中继器链。因此，这些算法可以作为分析大型量子中继器链协议和未来量子互联网拓扑的有用工具。