Measurement-Induced Entanglement Phase Transition in Random Bilocal Circuits

TL;DR

This paper investigates measurement-induced entanglement phase transitions in a random all-to-all interacting quantum circuit model, revealing two distinct phases characterized by different entropy behaviors and critical phenomena.

Contribution

It introduces an analytically tractable large-N model mapping to a quantum chain, providing new insights into phase transition characteristics in measurement-driven entanglement dynamics.

Findings

Identified two phases with distinct entropy behaviors.

Discovered a first-derivative discontinuity in the entropy in one phase.

Mapped the model to a one-dimensional quantum chain for analytical study.

Abstract

Measurement-induced entanglement phase transitions, caused by the competition between entangling unitary dynamics and disentangling projective measurements, have been studied in various random circuit models in recent years. In this paper, we study the dynamics of averaged purity for a simple $N$-qudit Brownian circuit model with all-to-all random interaction and measurements. In the large-$N$ limit, our model is mapped to a one-dimensional quantum chain in the semi-classical limit, which allows us to analytically study critical behaviors and various other properties of the model. We show that there are two phases distinguished by the behavior of the total system entropy in the long time. In addition, the two phases also have distinct subsystem entropy behavior. The low measurement rate phase has a first-derivative discontinuity in the behavior of second Renyi entropy versus subsystem size, similar to the "Page curve" of a random state, while the other phase has a smooth entropy curve.