Measurement induced phase transition in the central spin model: second R\'enyi entropy in dual space approach

TL;DR

This paper investigates measurement-induced phase transitions in the central spin model using second Rnyi entropy in dual space, revealing critical measurement rates that differ from simple mutual entropy predictions.

Contribution

It introduces a novel dual space approach to analyze entanglement phase transitions in the central spin model under measurement.

Findings

Critical measurement rates are identified.

Measurement rates differ from mutual entropy predictions.

Simulations include decoherence, relaxation, and gate errors.

Abstract

We conduct a numerical investigation of the dynamics of the central spin model in the presence of measurement processes. This model holds promise for experimental exploration due to its topology, which facilitates the natural distinction of a central particle and the quantum bath as different subsystems, allowing for the examination of entanglement phase transitions. To characterize the measurement-induced phase transition in this system, we employ a recently developed method based on second R\'enyi entropy in dual space. Our simulations account for decoherence, energy relaxation, and gate errors. We determine critical measurement rates and demonstrate that they significantly differ from those predicted by a simple approach based on mutual entropy.