Markovian Entanglement Dynamics under Locally Scrambled Quantum Evolution

TL;DR

This paper introduces a Markovian framework for understanding the evolution of quantum entanglement in locally scrambled quantum dynamics, utilizing an entanglement feature approach that maps entanglement properties to a many-body wave function.

Contribution

It develops a novel entanglement feature formulation and maps entanglement dynamics to an imaginary-time Schrödinger equation, enabling analysis of diverse random quantum dynamics.

Findings

Entanglement entropy follows Markovian dynamics under local scrambling.

The entanglement feature approach accurately predicts entanglement evolution.

Numerical simulations confirm the framework's validity for various models.

Abstract

We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a random ensemble that is invariant under local (on-site) basis transformations. In this case, the average entanglement entropy follows Markovian dynamics that the entanglement property of the future state can be predicted solely based on the entanglement properties of the current state and the unitary operator at each step. We introduce the entanglement feature formulation to concisely organize the entanglement entropies over all subsystems into a many-body wave function, which allows us to describe the entanglement dynamics using an imaginary-time Schr\"odinger equation, such that various tools developed in quantum many-body physics can be applied. The framework enables us to investigate a variety of random quantum dynamics beyond Haar random circuits and Brownian circuits. We perform numerical simulations for these models and demonstrate the validity and prediction power of the entanglement feature approach.