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：远程节点间共享的纠缠态常被用于量子网络应用。当量子资源充足时，可在网络中连续分布纠缠态，使节点能在需要时随时消耗这些纠缠态。这种纠缠的连续分布使得量子网络应用能够持续运行，同时定期获得纠缠态供应。本文重点研究连续分布纠缠协议的稳态性能分析，提出虚拟邻域尺寸和虚拟节点度数作为性能度量指标。我们利用帕累托最优概念构建多目标优化问题以实现性能最大化。以树形拓扑量子网络为例求解该问题。分析得出的主要结论之一是：纠缠消耗速率对协议性能的影响大于保真度要求。本文建立的度量指标可用于评估大规模量子网络纠缠分布协议的可行性。