Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit

TL;DR

This paper demonstrates that measurements in open quantum circuits can induce a stable, power-law scaling of entanglement negativity, counteracting decoherence effects, and reveals a phase transition to an area-law phase at higher measurement rates.

Contribution

It introduces a novel measurement-induced entanglement phase transition in open quantum circuits, with analytical and numerical evidence for power-law negativity scaling.

Findings

Power-law negativity scaling as L^{1/3} in steady state

Analytical mapping to directed polymers explains fluctuations

Transition to an area-law phase at higher measurement rates

Abstract

Generic many-body systems coupled to an environment lose their quantum entanglement due to decoherence and evolve to a mixed state with only classical correlations. Here, we show that measurements can stabilize quantum entanglement within open quantum systems. Specifically, in random unitary circuits with dephasing at the boundary, we find both numerically and analytically that projective measurements performed at a small nonvanishing rate results in a steady state with an $L^{1/3}$ power-law scaling entanglement negativity within the system. Using an analytical mapping to a statistical mechanics model of directed polymers in a random environment, we show that the power-law negativity scaling can be understood as Kardar-Parisi-Zhang fluctuations due to the random measurement locations. Further increasing the measurement rate leads to a phase transition into an area-law negativity phase, which is of the same universality as the entanglement transition in monitored random circuits without decoherence.