Emergent deterministic entanglement dynamics in monitored infinite-range bosonic systems

TL;DR

This paper demonstrates that in monitored infinite-range bosonic systems, quantum fluctuations follow deterministic dynamics in the thermodynamic limit, revealing exact solutions and explaining entanglement and phase transition phenomena.

Contribution

It introduces a semiclassical framework for deterministic quantum fluctuation dynamics in monitored bosonic systems, linking entanglement criticality with dissipative phase transitions.

Findings

Quantum fluctuations become deterministic in the thermodynamic limit.

Hierarchical equations explain entanglement and phase transition coincidence.

Exact solutions are provided for specific models like Bose-Hubbard dimer.

Abstract

We study monitored quantum dynamics of infinite-range interacting bosonic systems in the thermodynamic limit. We show that under semiclassical assumptions, the quantum fluctuations along single monitored trajectories adopt a deterministic limit for both quantum-jump and state-diffusion unravelings, and they can be exactly solved. In particular, the hierarchical structure of the equations of motion explains the coincidence of entanglement criticalities and dissipative phase transitions found in previous finite-size numerical studies. We illustrate the findings on a Bose-Hubbard dimer and a collective spin system.