Entanglement formation in continuous-variable random quantum networks

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. While previous works on quantum networks focus on discrete-variable systems, light--as the only travelling 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 and reveal unique phenomena. 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 dependent on the average squeezing density and strength.