Entanglement transitions and quantum bifurcations under continuous long-range monitoring

TL;DR

This paper investigates how continuous nonlocal measurements with power-law decay influence entanglement scaling and measurement distributions in free-fermionic quantum systems, revealing phase transitions in entanglement and measurement statistics.

Contribution

It introduces a detailed analysis of entanglement transitions under long-range monitoring, connecting measurement distribution changes to entanglement phases in quantum trajectories.

Findings

Volume-law entanglement for low decay exponent $eta$

Transition from subvolume to area-law entanglement at higher $eta$

Measurement distribution shifts from unimodal to bimodal at transition points

Abstract

We study the asymptotic bipartite entanglement entropy of the quantum trajectories of a free-fermionic system, when subject to a continuous nonlocal monitoring. The measurements are described by Gaussian-preserving two-point operators, whose strength decays as a power-law with exponent $\alpha$. Different behaviors of the entanglement entropy with the system size emerge: for $\alpha$ below a given threshold value a volume-law behavior sets in, while for larger $\alpha$ we observe a transition from subvolume to area-law, whose exact location depends on the measurements rate and on the presence of a Hamiltonian dynamics. We also consider the expectation probability distribution of the measurement operators, and find that this distribution features a transition from a unimodal to a bimodal shape. We discuss the possible connections between this qualitative change of the distribution and the entanglement transition points.