Entanglement formation in continuous-variable random quantum networks

Abstract

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 entanglement formation and networking 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 in general. In this work, 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. The entanglement distribution is directly connected to the probability distribution of the random walk, while the scrambling time is determined by the mixing time of the random walk. The dynamics of bipartite entanglement is determined by the boundary of the bipartition; An operational witness of multipartite entanglement, based on advantages in sensing tasks, is introduced to characterize the multipartite entanglement growth. A surprising linear superposition law in the entanglement growth is predicted by the theory and numerically verified, when the squeezers are sparse in space-time, despite the nonlinear nature of the entanglement dynamics. We also give exact solution to the equilibrium entanglement distribution (Page curves), including its fluctuations, and found various shapes dependent on the average squeezing density and strength.

15+3+2 pages, 24 figures

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• Non-unitary Entanglement Dynamics in Continuous Variable Systems
• Energy-dependent barren plateau in bosonic variational quantum circuits
• Exploring Shallow-Depth Boson Sampling: Towards Scalable Quantum Supremacy
• Information transmission with continuous variable quantum erasure channels
• A Survey on Continuous Variable Quantum Key Distribution for Secure Data Transmission: Toward the Future of Secured Quantum-Networks
• Average Rényi Entanglement Entropy in Gaussian Boson Sampling