Relaxation Critical Dynamics in Measurement-induced Phase Transitions

TL;DR

This paper studies the relaxation dynamics near measurement-induced phase transitions in quantum circuits, revealing different entanglement behaviors for various initial states and proposing a unified scaling framework that aids experimental detection.

Contribution

It introduces a unified scaling form for relaxation dynamics in MIPT, applicable to different initial states, and proposes a scheme to reduce post-selection overhead in experiments.

Findings

Entanglement entropy decays as t^{-1} for volume-law initial states.

Entanglement entropy grows as ln(t) for product initial states.

A unified scaling form describes relaxation behaviors across different initial states.

Abstract

Measurement-induced phase transition (MIPT) describes the nonanalytical change of the entanglement entropy resulting from the interplay between measurement and unitary evolution. In this paper, we investigate the relaxation critical dynamics near the MIPT for different initial states in a one-dimensional quantum circuit. Specifically, when the initial state is in the volume-law phase with vanishing measurement probability, we find that the half-chain entanglement entropy $S$ decays as $S\propto t^{-1}$ with the coefficients proportional to the size of the system in the short-time stage; In contrast, when the initial state is the product state, $S$ increases with time as $S\propto \ln{t}$, consistent with previous studies. Despite these contrasting behaviors, we develop a unified scaling form to describe these scaling behaviors for different initial states where the off-critical-point effects can also be incorporated. This framework offers significant advantages for experimental MIPT detection. Our novel scheme, leveraging relaxation dynamical scaling, drastically reduces post-selection overhead, and can eliminate it completely with trackable classical simulation.