发表机构
Politecnico di Milano; Universidad Politécnica de Madrid; University of Waterloo（米兰理工大学; 马德里理工大学; 滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对MDI-QKD网络规划，提出MHD问题并证明NP难，用MILP联合优化中心放置与用户分配，在城域拓扑中最小化可信中继需求。
AI 中文摘要
测量设备无关量子密钥分发（MDI-QKD）通过将测量委托给不可信中继来消除探测器侧信道漏洞，该中继在多个用户对共享时充当贝尔态测量（BSM）中心。信道损耗仍然限制了MDI-QKD链路的覆盖范围，因此长距离服务依赖可信中继进行密钥转发。随着MDI-QKD向城域部署推进，一个关键的网络规划问题浮现：如何在现有光纤基础设施上放置BSM中心以最小化可信中继的使用？在本工作中，我们将这一挑战形式化为MDI-QKD中心部署（MHD）问题。我们首先证明MHD问题是NP难的，然后将其表述为混合整数线性规划（MILP）。据我们所知，这是首个针对MDI-QKD网络规划的公式，它捕捉了MDI-QKD特有的结构特征，即共享BSM中心、两链路用户到中心路由以及损耗均衡约束，同时联合确定中心放置、用户到中心分配和可信中继需求分配。我们的解决方案考虑了现实的预算和容量约束，包括来自商业MDI-QKD解决方案实际部署的实用见解。在三个城域拓扑（12至50个节点）上以现实地理距离进行的数值评估表明，拓扑结构决定可信中继需求：中心放置本身在紧凑的城市网格中消除了所有可信中继，而在稀疏拓扑中，放宽损耗均衡约束消除了可信中继使用的主要来源，且无需额外基础设施成本。可信中继首次出现的密钥率阈值随网络直径（即任意节点对之间以光纤公里计的最大最短路径距离）单调变化，描绘了纯MDI-QKD部署的可行性边界。
英文摘要
Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) removes detector side-channel vulnerabilities by delegating measurements to an untrusted relay that, when shared by several user pairs, acts as a Bell-state measurement (BSM) hub. Channel loss still limits the reach of MDI-QKD links, so long-range services rely on trusted relays for key forwarding. As MDI-QKD moves toward metropolitan deployment, a key network-planning question arises: how should BSM hubs be placed on existing fiber infrastructure to minimize the use of trusted relays? In this work, we formalize this challenge as the MDI-QKD Hub Deployment (MHD) problem. We first prove that the MHD problem is NP-hard, and then formulate it as a Mixed-Integer Linear Programming (MILP). To the best of our knowledge, this is the first formulation for MDI-QKD network planning that captures the structural features specific to MDI-QKD, namely a shared BSM hub, two-link user-to-hub routing, and loss-balancing constraints, while jointly determining hub placement, user-to-hub assignment, and trusted-relay demand allocation. Our solution accounts for realistic budget and capacity constraints, including practical insights from real-world deployments of commercial MDI-QKD solutions. Numerical evaluations on three metropolitan topologies (12 to 50 nodes) at realistic geographic distances show that topology structure governs trusted-relay demand: hub placement alone eliminates all trusted relays in compact urban meshes, while in sparse topologies, relaxing the loss-balancing constraint removes the dominant source of trusted-relay usage at no additional infrastructure cost. The key-rate threshold at which trusted relays first appear shifts monotonically with the network diameter, i.e., the largest shortest-path distance between any node pair in fiber kilometers, delineating the feasibility boundary of pure MDI-QKD deployment.
Comments10 pages, 5 figures. Accepted to the IEEE International Conference on Quantum Computing and Engineering (QCE) 2026
