Entanglement is not only important for understanding the fundamental properties of many-body systems, but also the crucial resource enabling quantum advantages in practical information processing tasks. Although previous works on quantum networks focus on discrete-variable systems, light—as the only traveling carrier of quantum information in a network—is bosonic and thus requires a continuous-variable description. We extend the study to continuous-variable quantum networks. By mapping the ensemble-averaged entanglement dynamics on an arbitrary network to a random-walk process on a graph, we are able to exactly solve the entanglement dynamics. We identify squeezing as the source of entanglement generation, which triggers a diffusive spread of entanglement with a "parabolic light cone”. A surprising linear superposition law in the entanglement growth is predicted by the theory and numerically verified, despite the nonlinear nature of the entanglement dynamics. The equilibrium entanglement distribution (Page curves) is exactly solved and has various shapes depending on the average squeezing density and strength.

纠缠不仅对于理解多体系统的基本特性很重要，而且对于在实际信息处理任务中实现量子优势的关键资源也至关重要。尽管先前关于量子网络的工作都集中在离散变量系统上，但是光（作为网络中量子信息的唯一传播载体）是波色的，因此需要连续变量的描述。我们将研究扩展到连续变量量子网络。通过将任意网络上的集合平均纠缠动力学映射到图上的随机游走过程，我们能够精确地解决纠缠动力学。我们认为挤压是产生纠缠的根源，它会引发“抛物线形光锥”的纠缠扩散。尽管纠缠动力学具有非线性性质，但是该理论预测了纠缠增长中令人惊讶的线性叠加定律并进行了数值验证。精确地解决了平衡纠缠分布（Page曲线），并且根据平均挤压密度和强度，它具有各种形状。