Quantum repeater chains will form the backbone of future quantum networks that distribute entanglement between network nodes. Therefore, it is important to understand the entanglement distribution performance of quantum repeater chains, especially their throughput and latency. By using Markov chains to model the stochastic dynamics in quantum repeater chains, we offer analytical estimations for long-run throughput and on-demand latency of continuous entanglement distribution. We first study single-link entanglement generation using general multiheralded protocols. We then model entanglement distribution with entanglement swapping over two links, using either a single- or a double-heralded entanglement generation protocol. We also demonstrate how the two-link results offer insights into the performance of general $2^k$-link nested repeater chains. Our results enrich the quantitative understanding of quantum repeater network performance, especially the dependence on system parameters. The analytical formulae themselves are valuable reference resources for the quantum networking community. They can serve as benchmarks for quantum network simulation validation or as examples of quantum network dynamics modeling using the Markov chain formalism.

翻译：量子中继器链路将构成未来量子网络的骨干，用于在网络节点间分发纠缠。因此，理解量子中继器链路的纠缠分发性能，特别是其吞吐量和延迟，至关重要。通过使用马尔可夫链对量子中继器链路中的随机动力学进行建模，我们为连续纠缠分发的长期吞吐量和按需延迟提供了解析估计。我们首先研究了使用通用多预示协议的单链路纠缠生成。随后，我们使用单预示或双预示纠缠生成协议，对通过纠缠交换在两个链路上进行的纠缠分发进行了建模。我们还展示了如何利用双链路结果来洞察一般 $2^k$ 链路嵌套中继器链路的性能。我们的研究结果丰富了对量子中继器网络性能，特别是其对系统参数依赖性的定量理解。这些解析公式本身是量子网络领域宝贵的参考资源。它们可作为量子网络仿真验证的基准，或作为使用马尔可夫链形式体系对量子网络动力学进行建模的范例。