We investigate resource allocation for quantum entanglement distribution over an optical network. We characterize and model a network architecture that employs a single quasi-deterministic time-frequency heralded Einstein-Podolsky-Rosen (EPR) pair source, and develop a routing scheme for distributing entangled photon pairs over such a network. We focus on max-min fairness in entanglement distribution and compare the performance of various spectrum allocation schemes by examining the max-min and median number of EPR-pairs assigned by them, and the Jain index associated with this assignment. Since this presents an NP-hard problem, we identify two approximation algorithms that outperform others in minimum and mean EPR-pair rate distribution and are comparable to others in the Jain index. We also analyze how the network size and connectivity affect these metrics using Watts-Strogatz random graphs. We find that a spectrum allocation approach that achieves high minimum EPR-pair rate can perform significantly worse when the median EPR-pair rate, Jain index, and runtimes are considered.

翻译：我们研究了光网络上量子纠缠分发的资源分配问题。我们描述并建模了一种采用单一准确定性时频预示爱因斯坦-波多尔斯基-罗森（EPR）对源的网络架构，并为此类网络开发了纠缠光子对分发的路由方案。我们重点关注纠缠分发中的最大最小公平性，通过比较不同频谱分配方案所分配的最大最小EPR对数量、中位数EPR对数量以及与此分配相关的Jain指数来评估其性能。由于该问题属于NP难问题，我们确定了两种在最小和平均EPR对速率分配方面优于其他算法，且在Jain指数方面与其他算法相当的近似算法。我们还利用Watts-Strogatz随机图分析了网络规模和连接性对这些指标的影响。研究发现，在考虑中位数EPR对速率、Jain指数和运行时间时，实现高最小EPR对速率的频谱分配方案可能表现显著较差。