In research concerning quantum networks, it is often assumed that the parties can classically communicate with each other. However, classical communication might introduce a substantial delay to the network, especially if it is large. As the latency of a network is one of its most important characteristics, it is interesting to consider quantum networks in which parties cannot communicate classically and ask what limitations this assumption imposes on the possibility of preparing multipartite states in such networks. We show that graph states of an arbitrary prime local dimension known for their numerous applications in quantum information cannot be generated in a quantum network in which parties are connected via sources of bipartite quantum states and the classical communication is replaced by some pre-shared classical correlations. We then generalise our result to arbitrary quantum states that are sufficiently close to graph states.

在有关量子网络的研究中，通常假设各方可以经典地相互通信。然而，经典通信可能会给网络带来很大的延迟，尤其是在网络很大的情况下。由于网络的延迟是其最重要的特征之一，因此考虑各方无法进行经典通信的量子网络并询问该假设对在此类网络中准备多方状态的可能性施加了哪些限制是很有趣的。我们证明，以其在量子信息中的众多应用而闻名的任意素局部维度的图状态不能在量子网络中生成，在该网络中，各方通过二分量子态源连接，并且经典通信被一些预先共享的经典关联所取代。然后，我们将结果推广到足够接近图状态的任意量子态。