# Multipartite-Entanglement Dynamics in Regular-to-Ergodic Transition: a Quantum-Fisher-Information approach

## TL;DR

This paper uses quantum Fisher information to analyze multipartite entanglement dynamics during the regular-to-ergodic transition in the Dicke model, revealing how entanglement and metrological usefulness evolve across the transition.

## Contribution

It introduces quantum Fisher information as a tool to study entanglement dynamics in many-body systems and demonstrates its effectiveness in characterizing the regular-to-ergodic transition.

## Key findings

- QFI exhibits distinct dynamical behavior across the transition
- Asymptotic QFI and timescales depend on interaction strength and system size
- Ergodic dynamics produce faster, more useful entangled states for metrology

## Abstract

The characterization of entanglement is a central problem for the study of quantum many-body dynamics. Here, we propose the quantum Fisher information as a useful tool for the study of multipartite-entanglement dynamics in many-body systems. We illustrate this by considering the regular-to-ergodic transition in the Dicke model---a fully-connected spin model showing quantum thermalization above a critical interaction strength. We show that the QFI has a rich dynamical behavior which drastically changes across the transition. In particular, the asymptotic value of the QFI, as well as its characteristic timescales, witness the transition both through their dependence on the interaction strength and through the scaling with the system size. Since the QFI also sets the ultimate bound for the precision of parameter estimation, it provides a metrological perspective on the characterization of entanglement dynamics in many-body systems. Here we show that quantum ergodic dynamics allows for a much faster production of metrologically useful states.