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. 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.

Fast decay of classification error in variational quantum circuits

“…This shows a limitation of those over-simplified ansatzs. Due to nonlocal gates, prism and polygon have slight advantages in error probability over the brickwall architecture, consistent with their scrambling powers [45][46][47][48][49], as verified by operator size calculations in Sec. V B.…”

Quantum Metrological Power of Continuous-Variable Quantum Networks

“…Since they achieve the Heisenberg scaling on average, quantum networks of local beam splitters constitute sufficient entanglement on average as expected in Ref. [38]; namely, large entanglement can be obtained for a depth D ∝ M 2 .…”

“…Local beam splitter network.-While a global random BSN is suitable to model a sufficiently complex CV network, it is also crucial to investigate how complicated the network has to be to attain a metrological enhancement from a practical perspective. To do that, we study a CV quantum network composed of a local random BSN instead of a global random BSNs [37][38][39], which is depicted in Fig. 3 (a).…”

Information transmission with continuous variable quantum erasure channels

“…Unlike the DV case, the CV system is infinite dimensional, which might involve unbounded energy [27]. The unitary group for fully scrambling the system is generally noncompact [26,35], e.g., the Gaussian unitary with squeezing forms a noncompact group. A natural guess is to use random passive unitary U c (without squeezing, it forms a compact group) to scramble those Bosonic modes.…”