Statistical Mechanics of Monitored Dissipative Random Circuits

TL;DR

This paper investigates how dissipation affects measurement-induced entanglement transitions in monitored quantum circuits by mapping the problem to a classical 2D Ising model with symmetry-breaking interactions.

Contribution

It extends the classical spin model mapping to include on-site dissipation, providing new insights into entanglement dynamics in realistic open quantum systems.

Findings

Dissipation modifies the entanglement phase transition behavior.

Different dynamical regimes are characterized by classical domain wall configurations.

The analysis applies to monitored open quantum systems and small system sizes.

Abstract

Dissipation is inevitable in realistic quantum circuits. We examine the effects of dissipation on a class of monitored random circuits that exhibit a measurement-induced entanglement phase transition. This transition has previously been understood as an order-to-disorder transition of an effective classical spin model. We extend this mapping to include on-site dissipation described by the dephasing and spontaneous emission channel and study the corresponding 2D Ising model with $\mathbb{Z}_2$-symmetry-breaking interactions. We analyze the dynamical regimes of the mutual information and find that the joint action of monitored measurements and dissipation yields short time, intermediate time and steady state behavior that can be understood in terms of crossovers between different classical domain wall configurations. The presented analysis applies to monitored open or Lindbladian quantum systems and provides a tool to understand entanglement dynamics in realistic dissipative settings and small achievable system sizes.