The entanglement swapping protocol (ESP) is a fundamental primitive for distributing quantum correlations across distant nodes in a quantum network. Recent studies have demonstrated that even when the involved qubit pairs are only partially entangled, it is still possible to concentrate and transmit entanglement via Bell-basis measurements. In this work, we extend these ideas to quantum networks with various topologies--including linear, star, and hybrid configurations--by analysing the application of the ESP to initially partially entangled pure states. We investigate how entanglement evolves under such protocols by considering the transformations of the initial states and evaluating the success probabilities for generating maximally entangled states at the output. Our results offer new insights into the dynamics of the entanglement distribution in quantum networks.

翻译：纠缠交换协议（ESP）是量子网络中跨越远程节点分发量子关联的基础原语。近期研究表明，即便所涉及的量子比特对仅处于部分纠缠态，仍可通过贝尔基测量实现纠缠的集中与传输。本研究将这一思路拓展至包含线性、星型和混合配置等多种拓扑结构的量子网络，通过分析对初始部分纠缠纯态应用ESP的过程，探讨了此类协议下纠缠的演化规律——具体包括初始态变换的考察以及输出端生成最大纠缠态的成功概率评估。我们的结果为量子网络中纠缠分发的动力学机制提供了全新洞见。