Purification and scrambling in a chaotic Hamiltonian dynamics with measurements

TL;DR

This paper investigates how measurements influence purification dynamics and information spreading in a chaotic transverse-field Ising model, revealing a measurement-induced phase transition and differences between chaotic and integrable regimes.

Contribution

It introduces a formalism for tripartite mutual information in non-unitary dynamics and demonstrates a measurement-induced phase transition with distinct spatial information patterns.

Findings

Existence of a measurement-induced phase transition between mixed and purified phases

Spatial patterns of information spreading are preserved but slowed by measurements

Differences in information propagation distinguish chaotic from integrable regimes

Abstract

Chaotic transverse-field Ising model with measurements exhibits interesting purification dynamics. Ensemble of non-unitary dynamics of a chaotic many-body system with measurements exhibits a purification phase transition. We numerically find that the law of the increase dynamics of the purity changes by projective measurements in the model. In order to study this behavior in detail, we construct the formalism of the tripartite mutual information (TMI) for non-unitary time evolution operator by using the state-channel map. The numerical result of the saturation value of the TMI indicates the existence of a measurement-induced phase transition. This implies the existence of two distinct phases, mixed phase and purified phase. Furthermore, the real-space spread of the TMI is investigated to explore spatial patterns of information spreading. Even in the purified phase, the spatial pattern of the light cone spread of quantum information is not deformed, but its density of information propagation is reduced on average by the projective measurements. We also find that this spatial pattern of the TMI distinguishes the chaotic and integrable regimes of the system.