Non-unitary Entanglement Dynamics in Continuous Variable Systems

TL;DR

This paper investigates entanglement dynamics in continuous-variable systems under Gaussian measurements, revealing that steady state entanglement saturates to an area-law and lacks a transition, contrasting with qubit systems.

Contribution

It introduces a random Gaussian circuit model for CV systems with measurements and analyzes entanglement behavior, highlighting differences from qubit systems due to unbounded local Hilbert spaces.

Findings

Steady state entanglement saturates to an area-law with nonzero measurement rate.

No entanglement transition occurs in Gaussian CV dynamics.

Entanglement destruction occurs faster than buildup due to unbounded local Hilbert space.

Abstract

We construct a random unitary Gaussian circuit for continuous-variable (CV) systems subject to Gaussian measurements. We show that when the measurement rate is nonzero, the steady state entanglement entropy saturates to an area-law scaling. This is different from a many-body qubit system, where a generic entanglement transition is widely expected. Due to the unbounded local Hilbert space, the time scale to destroy entanglement is always much shorter than the one to build it, while a balance could be achieved for a finite local Hilbert space. By the same reasoning, the absence of transition should also hold for other non-unitary Gaussian CV dynamics.