Entanglement entropy scaling transition under competing monitoring protocols

TL;DR

This paper investigates how competing continuous monitoring protocols influence entanglement entropy scaling in quantum systems, revealing a transition from critical to area-law behavior driven by measurement-induced effects.

Contribution

It introduces a novel analysis of entanglement scaling transitions caused by incompatible monitoring protocols, extending understanding of measurement-induced phase transitions.

Findings

Entanglement entropy transitions from critical to area-law scaling.

Competing dissipation channels can induce a phase transition in entanglement.

Measurement protocols can be engineered to control quantum entanglement.

Abstract

Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works has been primarily on engineering the non-equilibrium steady state, we investigate the build-up of entanglement in the quantum trajectories. Specifically, we analyze the competition between two different dissipation channels arising from two incompatible continuous monitoring protocols. The first protocol locks the phase of neighboring sites upon registering a quantum jump, thereby generating a long-range entanglement through the system, while the second destroys the coherence via a dephasing mechanism. By studying the unraveling of stochastic quantum trajectories associated with the continuous monitoring protocols, we present a transition for the scaling of the averaged trajectory entanglement entropies, from critical scaling to area-law behavior. Our work provides an alternative perspective on the measurement-induced phase transition: the measurement can be viewed as monitoring and registering quantum jumps, offering an intriguing extension of these phase transitions through the long-established realm of quantum optics.