Quantum networks will allow to implement communication tasks beyond the reach of their classical counterparts. A pressing and necessary issue for the design of quantum network protocols is the quantification of the rates at which these tasks can be performed. Here, we propose a simple recipe that yields efficiently computable lower and upper bounds on the maximum achievable rates. For this we make use of the max-flow min-cut theorem and its generalization to multi-commodity flows to obtain linear programs. We exemplify our recipe deriving the linear programs for bipartite settings, settings where multiple pairs of users obtain entanglement in parallel as well as multipartite settings, covering almost all known situations. We also make use of a generalization of the concept of paths between user pairs in a network to Steiner trees spanning a group of users wishing to establish Greenberger-Horne-Zeilinger states.

量子网络将允许执行通信任务，超出传统通信对象的范围。设计量子网络协议的一个紧迫而必要的问题是量化执行这些任务的速率。在这里，我们提出了一个简单的方法，可以有效地计算出最大可达到速率的上下限。为此，我们利用最大流量最小割定理及其对多商品流的推广来获得线性程序。我们以配方为例，推导了用于二分设置，多对用户并行获得缠结的设置以及多分设置的线性程序，涵盖几乎所有已知情况。