In quantum networks, one way to communicate is to distribute entanglements through swapping at intermediate nodes. Most existing work primarily aims to create efficient two-party end-to-end entanglement over long distances. However, some scenarios also require remote multipartite entanglement for applications such as quantum secret sharing and multi-party computation. Our previous study improved end-to-end entanglement rates using an asynchronous, tree-based routing scheme that relies solely on local knowledge of entanglement links, conserving unused entanglement and avoiding synchronous operations. This article extends this approach to multipartite entanglements, particularly the three-party Greenberger-Horne-Zeilinger (GHZ) states. It shows that our asynchronous protocol outperforms traditional synchronous methods in entanglement rates, especially as coherence times increase. This approach can also be extended to four-party and larger multipartite GHZ states, highlighting the effectiveness and adaptability of asynchronous routing for multipartite scenarios across various network topologies.

翻译：在量子网络中，一种通信方式是通过中间节点的交换来分发纠缠。现有工作主要聚焦于在长距离上建立高效的两方端到端纠缠。然而，某些场景也需要远程多方纠缠，以支持诸如量子秘密共享和多方计算等应用。我们先前的研究利用一种基于异步、树状的路由方案，仅依靠对纠缠链接的局部知识，提升了端到端纠缠速率，同时节约了未使用的纠缠并避免了同步操作。本文将这一方法扩展至多方纠缠，特别是三方Greenberger-Horne-Zeilinger (GHZ)态。研究表明，我们的异步协议在纠缠速率上优于传统同步方法，尤其当相干时间增加时更为明显。该方法还可扩展至四方及更大规模的多方GHZ态，突显了异步路由在各种网络拓扑中处理多方场景的有效性与适应性。