Entangled states shared among distant nodes are frequently used in quantum network applications. When quantum resources are abundant, entangled states can be continuously distributed across the network, allowing nodes to consume them whenever necessary. This continuous distribution of entanglement enables quantum network applications to operate continuously while being regularly supplied with entangled states. Here, we focus on the steady-state performance analysis of protocols for continuous distribution of entanglement. We propose the virtual neighborhood size and the virtual node degree as performance metrics. We utilize the concept of Pareto optimality to formulate a multi-objective optimization problem to maximize the performance. As an example, we solve the problem for a quantum network with a tree topology. One of the main conclusions from our analysis is that the entanglement consumption rate has a greater impact on the protocol performance than the fidelity requirements. The metrics that we establish in this manuscript can be utilized to assess the feasibility of entanglement distribution protocols for large-scale quantum networks.

翻译：远距离节点间共享的纠缠态在量子网络应用中频繁使用。当量子资源充足时，纠缠态可在网络中连续分布，使节点能够随时按需消耗。这种连续纠缠分布使得量子网络应用在持续获得纠缠态供给的同时保持不间断运行。本文聚焦于连续纠缠分布协议的稳态性能分析，提出虚拟邻域规模与虚拟节点度作为性能指标，并利用帕累托最优概念构建多目标优化问题以最大化性能。以树形拓扑量子网络为例进行求解，主要结论表明：纠缠消耗率对协议性能的影响显著大于保真度要求。本文确立的指标可用于评估大规模量子网络中纠缠分布协议的可行性。