Measurement-induced purification in large-N hybrid Brownian circuits

TL;DR

This paper investigates a measurement-induced entanglement phase transition in a large-N all-to-all Brownian circuit model, revealing a second-order transition characterized by replica symmetry breaking and critical properties akin to a 0+1D Ising field theory.

Contribution

It provides an analytically tractable model demonstrating a measurement-induced phase transition, including a detailed saddle-point analysis and connections to quantum error correction.

Findings

Identifies a second-order phase transition in the purity of the system.

Characterizes the critical behavior using a 0+1D Ising field theory.

Corroborates theoretical results with exact diagonalization.

Abstract

Competition between unitary dynamics that scrambles quantum information non-locally and local measurements that probe and collapse the quantum state can result in a measurement-induced entanglement phase transition. Here we study this phenomenon in an analytically tractable all-to-all Brownian hybrid circuit model composed of qubits. The system is initially entangled with an equal sized reference, and the subsequent hybrid system dynamics either partially preserves or totally destroys this entanglement depending on the measurement rate. Our approach can access a variety of entropic observables which are distinguished by the averaging procedure, and for concreteness we focus on a particular purity quantity for which the averaging is particularly simple. We represent the purity as a path integral coupling four replicas with twisted boundary conditions. Saddle-point analysis reveals a second-order phase transition corresponding to replica permutation symmetry breaking below a critical measurement rate. The transition is mean-field-like and we characterize the critical properties near the transition in terms of a simple Ising field theory in 0+1 dimensions. In addition to studying the purity of the entire system, we study subsystem purities and relate these results to manifestations of quantum error correction in the model. We also comment on the experimental feasibility for simulating this averaged purity, and corroborate our results with exact diagonalization for modest system sizes.