A quantum network distributes quantum entanglements between remote nodes, and is key to many applications in secure communication, quantum sensing and distributed quantum computing. This paper explores the fundamental trade-off between the throughput and the quality of entanglement distribution in a multi-hop quantum repeater network. Compared to existing work which aims to heuristically maximize the entanglement distribution rate (EDR) and/or entanglement fidelity, our goal is to characterize the maximum achievable worst-case fidelity, while satisfying a bound on the maximum achievable expected EDR between an arbitrary pair of quantum nodes. This characterization will provide fundamental bounds on the achievable performance region of a quantum network, which can assist with the design of quantum network topology, protocols and applications. However, the task is highly non-trivial and is NP-hard as we shall prove. Our main contribution is a fully polynomial-time approximation scheme to approximate the achievable worst-case fidelity subject to a strict expected EDR bound, combining an optimal fidelity-agnostic EDR-maximizing formulation and a worst-case isotropic noise model. The EDR and fidelity guarantees can be implemented by a post-selection-and-storage protocol with quantum memories. By developing a discrete-time quantum network simulator, we conduct simulations to show the characterized performance region (the approximate Pareto frontier) of a network, and demonstrate that the designed protocol can achieve the performance region while existing protocols exhibit a substantial gap.

翻译：量子网络在远程节点间分发量子纠缠态，是安全通信、量子传感和分布式量子计算等诸多应用的关键。本文研究多跳量子中继网络中纠缠分发的吞吐量与质量之间的基本权衡。与现有旨在启发式最大化纠缠分发速率（EDR）和/或纠缠保真度的工作不同，我们的目标是刻画在满足任意一对量子节点间最大可达期望EDR约束下的最坏情况保真度的最大值。这一刻画将为量子网络的性能可达区域提供基本界限，有助于量子网络拓扑、协议和应用的设计。然而，正如我们将证明的，该任务极具挑战性且为NP难问题。我们的主要贡献是提出一种完全多项式时间近似方案，用于近似满足严格期望EDR约束下的可达到的最坏情况保真度，该方法结合了最优的保真度无关的EDR最大化公式和一种各向同性噪声模型。通过带有量子存储器的后选择与存储协议，可实现EDR与保真度的保证。通过开发离散时间量子网络模拟器，我们进行了仿真，展示了网络的性能可达区域（近似帕累托前沿），并证明所设计的协议能够达到该性能区域，而现有协议存在显著差距。