Enhanced entanglement negativity in boundary driven monitored fermionic chains

TL;DR

This paper demonstrates that weak monitoring in boundary-driven fermionic chains enhances long-term entanglement negativity, contrasting with unitary evolution, and reveals a transition from logarithmic to area-law scaling with monitoring strength.

Contribution

It uncovers the dual role of weak monitoring in open quantum systems, showing entanglement enhancement and a phase transition in negativity and mutual information.

Findings

Monitoring enhances entanglement negativity at long times.

Negativity scales logarithmically with system size at low monitoring strength.

A transition to area-law scaling occurs as monitoring strength increases.

Abstract

We investigate entanglement dynamics in continuously monitored open quantum systems featuring current-carrying non-equilibrium states. We focus on a prototypical one-dimensional model of boundary-driven non-interacting fermions with monitoring of the local density, whose average Lindblad dynamics features a well-studied ballistic to diffusive crossover in transport. Here we analyze the dynamics of the fermionic negativity, mutual information, and purity along different quantum trajectories. We show that monitoring this boundary-driven system enhances its entanglement negativity at long times, which otherwise decays to zero in absence of measurements. This result is in contrast with the case of unitary evolution where monitoring suppresses entanglement production. For small values of $\gamma$, the stationary-state negativity shows a logarithmic scaling with system size, transitioning to an area-law scaling as $\gamma$ is increased beyond a critical value. Similar critical behavior is found in the mutual information, while the late-time purity shows no apparent signature of a transition, being $O(1)$ for all values of $\gamma$. Our work unveils the double role of weak monitoring in current-driven open quantum systems, simultaneously damping transport and enhancing entanglement.