Entanglement between quantum network nodes is often produced using intermediary devices - such as heralding stations - as a resource. When scaling quantum networks to many nodes, requiring a dedicated intermediary device for every pair of nodes introduces high costs. Here, we propose a cost-effective architecture to connect many quantum network nodes via a central quantum network hub called an Entanglement Generation Switch (EGS). The EGS allows multiple quantum nodes to be connected at a fixed resource cost, by sharing the resources needed to make entanglement. We propose an algorithm called the Rate Control Protocol (RCP) which moderates the level of competition for access to the hub's resources between sets of users. We proceed to prove a convergence theorem for rates yielded by the algorithm. To derive the algorithm we work in the framework of Network Utility Maximization (NUM) and make use of the theory of Lagrange multipliers and Lagrangian duality. Our EGS architecture lays the groundwork for developing control architectures compatible with other types of quantum network hubs as well as system models of greater complexity.

翻译：量子网络节点间的纠缠通常借助中介设备（如信令站）作为资源来产生。当量子网络扩展到多个节点时，为每一对节点配置专用中介设备会带来高昂成本。为此，我们提出一种经济高效的控制架构，通过一个称为纠缠生成开关（EGS）的中央量子网络集线器连接多个量子节点。EGS通过共享生成纠缠所需的资源，使得多个量子节点能够以固定资源成本实现互联。我们提出一种名为速率控制协议（RCP）的算法，该算法可调节不同用户组之间对集线器资源访问的竞争程度。随后，我们证明该算法产生的速率收敛定理。为推导该算法，我们采用网络效用最大化（NUM）框架，并借助拉格朗日乘子法和拉格朗日对偶理论。我们的EGS架构为开发与其他类型量子网络集线器及更复杂系统模型兼容的控制架构奠定了基础。