Information Scrambling in Bosonic Gaussian Dynamics

TL;DR

This paper studies how information spreads in bosonic Gaussian systems with quadratic Hamiltonians, revealing scrambling behaviors similar to chaotic systems even in integrable regimes, with implications for quantum information processing.

Contribution

It demonstrates that Gaussian dynamics can exhibit information scrambling akin to chaos, highlighting the role of randomness and Gaussian states in continuous-variable quantum systems.

Findings

Memory effects vanish in entanglement dynamics under Gaussian random local evolution.

Tripartite mutual information saturates at large negative values, indicating scrambling.

Gaussian systems can show chaotic features when non-Gaussian states are considered.

Abstract

We investigate the dynamics of information scrambling in bosonic systems undergoing Gaussian unitary evolution associated with quadratic Hamiltonians. For initial Gaussian states, we observe the disappearance of the memory effect in the entanglement dynamics of disjoint blocks under Gaussian random local dynamics. In addition, we show that randomness in the Hamiltonian causes the tripartite mutual information to saturate at relatively large negative values. Therefore, despite being integrable, these systems exhibit information-scrambling diagnostics that mirror those observed in chaotic systems. We note, however, that random quadratic Hamiltonians can have a component exhibiting Wigner-Dyson energy-level statistics; for non-Gaussian states within the corresponding subspace, these systems can display chaotic behavior. Our results provide insight into the Gaussian dynamics of continuous-variable systems, which are useful and available resources for quantum information processing.