We study a quantum network that distributes entangled quantum states to multiple sets of users that are connected to the network. Each user is connected to a switch of the network via a link. All the links of the network generate bipartite Bell-state entangled states in each time-slot with certain probabilities, and each end node stores one qubit of the entanglement generated by the link. To create shared entanglements for a set of users, measurement operations are performed on qubits of link-level entanglements on a set of related links, and these operations are probabilistic in nature and are successful with certain probabilities. Requests arrive to the system seeking shared entanglements for different sets of users. Each request is for the creation of shared entanglements for a fixed set of users using link-level entanglements on a fixed set of links. Requests are processed according to First-Come-First-Served service discipline and unserved requests are stored in buffers. Once a request is selected for service, measurement operations are performed on qubits of link-level entanglements on related links to create a shared entanglement. For given set of request arrival rates and link-level entanglement generation rates, we obtain necessary conditions for the stability of queues of requests. In each time-slot, the scheduler has to schedule entanglement swapping operations for different sets of users to stabilize the network. Next, we propose a Max-Weight scheduling policy and show that this policy stabilizes the network for all feasible arrival rates. We also provide numerical results to support our analysis. The analysis of a single quantum switch that creates multipartite entanglements for different sets of users is a special case of our work.

中文翻译：

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具有最大权重调度的量子网络稳定性分析

我们研究了一个量子网络，该网络将纠缠的量子态分布到连接到网络的多组用户。每个用户通过链路连接到网络的交换机。网络的所有链路在每个时隙内以一定的概率产生二分贝尔态纠缠态，每个端节点存储链路产生纠缠态的一个量子比特。为了为一组用户创建共享纠缠，对一组相关链路上的链路级纠缠的量子位进行测量操作，这些操作本质上是概率性的，并以一定的概率成功。请求到达系统以寻求不同用户组的共享纠缠。每个请求都是为了使用一组固定链接上的链接级纠缠为一组固定用户创建共享纠缠。根据先来先服务的服务原则处理请求，未提供服务的请求存储在缓冲区中。一旦选择了服务请求，就会对相关链路上的链路级纠缠的量子位执行测量操作，以创建共享纠缠。对于给定的一组请求到达率和链路级纠缠生成率，我们获得了请求队列稳定性的必要条件。在每个时隙中，调度器必须为不同的用户组调度纠缠交换操作以稳定网络。接下来，我们提出了一个最大权重调度策略，并表明该策略可以稳定所有可行到达率的网络。我们还提供数值结果来支持我们的分析。对为不同用户组创建多部分纠缠的单个量子开关的分析是我们工作的一个特例。