发表机构
Institute of Physics, Slovak Academy of Sciences（斯洛伐克科学院物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对纠缠网络的无源波长路由问题，基于连通图建立资源优化模型，得出单侧及共轭波长扇出下的精确资源定律，明确了频谱效率等参数的竞争关系，为无源纠缠架构设计提供了直接途径。
AI 中文摘要
基于纠缠的网络通过在互连节点间无源路由频谱关联的光子对，为多用户量子通信提供了可扩展框架。多项波长分配方案已得到实验验证，但这些设计尚未给出频谱使用、接收机负载、重复连接与扇出之间相互约束的通用确定方法。我们通过网络的连通图解决该问题，其中波长分配成为资源优化问题。对于单侧扇出，将每条链路分配给一个中心并将具有相同中心的链路分组，可对任意网络和扇出限制实现精确优化。我们针对完全网络及每个用户均有一个排除伙伴的完全网络求解该问题。允许两个共轭波长扇出会改变资源格局：平衡二叉层级结构可实现完全网络的最小频谱层数量，同时将最大接收机负载降至用户数量的对数级。八用户完全网络明确了频谱效率、接收机负载、冗余度与扇出的竞争关系。我们计入无源分路器损耗及密钥率对所传输光子对通量的依赖，以确定满足规定目标所需的最小总光子对产生率。最后，我们针对连续波泵浦的宽带源，构建了相应的BBM92量子密钥分发（QKD）安全密钥率分析，在两个端点用户的探测器通道间评估真实与偶然符合事件，且相对层光子对产生率由源光谱确定。因此，该框架提供了从精确网络资源定律到实验硬件约束下无源纠缠架构设计与比较的直接途径。
英文摘要
Entanglement-based networks provide a scalable framework for multiuser quantum communication by passively routing spectrally correlated photon pairs across interconnected nodes. Several wavelength-allocation schemes have been demonstrated experimentally, but these designs do not yet give a general way to determine how spectral use, receiver load, repeated connections, and fan-out constrain one another. We address this problem through the network's connectivity graph, where the wavelength assignment becomes a resource-optimization problem. For one-sided fan-out, assigning each link to a center and grouping links with the same center gives an exact optimization for arbitrary networks and fan-out limits. We solve this for complete networks and for complete networks in which every user has one excluded partner. Allowing both conjugate wavelengths to fan out changes the resource landscape: a balanced binary hierarchy attains the minimum spectral-layer count for a complete network while reducing the maximum receiver load to logarithmic in the number of users. An eight-user complete network then makes explicit the competing roles of spectral efficiency, receiver load, redundancy, and fan-out. We include the passive-splitter loss and the dependence of the key rate on the delivered pair flux to determine the minimum total pair-generation rate required to meet the prescribed targets. Finally, we formulate the corresponding BBM92 quantum key distribution (QKD) secret-key-rate analysis for a continuous-wave-pumped broadband source, with true and accidental coincidences evaluated between detector channels at the two endpoint users and relative layer pair-generation rates fixed by the source spectrum. This framework, therefore, provides a direct route from exact network resource laws to the design and comparison of passive entanglement architectures under experimentally specified hardware constraints.
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