Estimation of the geometric measure of entanglement with Wehrl Moments through Artificial Neural Networks

TL;DR

This paper demonstrates that artificial neural networks can accurately estimate the geometric measure of entanglement in symmetric multiqubit states using Wehrl moments, offering a practical alternative to full quantum state tomography.

Contribution

It introduces a neural network approach to predict entanglement measures from Wehrl moments, outperforming convergence acceleration methods and proposing an experimental measurement protocol.

Findings

ANNs accurately predict entanglement from Wehrl moments

ANNs outperform convergence acceleration algorithms with limited data

Proposes a state-independent protocol for Wehrl moment measurement

Abstract

In recent years, artificial neural networks (ANNs) have become an increasingly popular tool for studying problems in quantum theory, and in particular entanglement theory. In this work, we analyse to what extent ANNs can accurately predict the geometric measure of entanglement of symmetric multiqubit states using only a limited number of Wehrl moments (moments of the Husimi function of the state) as input, which represents partial information about the state. We consider both pure and mixed quantum states. We compare the results we obtain by training ANNs with the informed use of convergence acceleration methods. We find that even some of the most powerful convergence acceleration algorithms do not compete with ANNs when given the same input data, provided that enough data is available to train these ANNs. We also provide an experimental protocol for measuring Wehrl moments, which is state-independent. More generally, this work opens up perspectives for the estimation of entanglement measures and other SU(2)-invariant quantities, such as the Wehrl entropy, in a way that is more accessible in experiments than by means of full state tomography.