Entanglement formation in continuous-variable random quantum networks

Bingzhi Zhang,Quntao Zhuang

doi:10.1038/s41534-021-00370-w

Bingzhi Zhang, Quntao Zhuang

Open Access

https://doi.org/10.1038/s41534-021-00370-w

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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. 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.

Highlights

Quantum information science has brought to us capabilities to enhance the performance of computing[1], sensing[2], and communication[3,4], through entangling local or distant processing nodes
The study of entanglement formation and quantum information scrambling has been fruitful in complex systems such as random quantum networks[9,10,11], and circuits[12,13,14,15,16], many-body systems[17,18,19,20,21,22,23,24,25,26], quantum graphs[27,28,29], models of holography[30,31,32,33], and quantum gravity[34,35,36,37,38,39,40,41,42,43,44,45,46]
We study quantum information scrambling in CV quantum networks focusing on the entanglement formation dynamics

Summary

INTRODUCTION

Quantum information science has brought to us capabilities to enhance the performance of computing[1], sensing[2], and communication[3,4], through entangling local or distant processing nodes. Various applications in the photonic or microwave domain, including clusterstate-based quantum computing[53], quantum sensing applications[54,55,56,57,58,59,60,61], and entanglement-assisted communication[62,63], require CV entanglement in the form of Gaussian states[64] In this regard, noiseless linear amplifiers[65] and error correction codes[66,67] provide initial tools for CV networking, and an out-of-time-order correlator (OTOC) has revealed a squeezing-dependent butterflyvelocity of operator spreading[68]. To produce the Gaussian states that enable various applications in communication, sensing, and computing, we consider Gaussian unitaries[64], which are unitaries generated by Hamiltonians that are second order in the quadrature operators

RESULTS

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