Universal Relation Between Quantum Entanglement and Particle Transport

TL;DR

This paper reveals a universal link between entanglement entropy and particle transport in a 1D Fermi-Hubbard system, using machine learning and analytical models to predict quantum correlations.

Contribution

It introduces a universal relationship between entanglement and particle transport, learned via a novel machine learning approach, and proposes an analytical expression to describe this correlation.

Findings

Machine learning accurately predicts entanglement from particle transport data.

A simple analytical formula captures the entanglement-transport relationship.

The results apply across various interaction strengths in the system.

Abstract

Entanglement entropy is a fundamental measure of quantum correlations and a key resource underpinning advances in quantum information and many-body physics. We uncover a universal relationship between bipartite entanglement entropy and particle number after the barrier in a one-dimensional Fermi-Hubbard system with an external asymmetric potential. Using Kolmogorov-Arnold Networks - a novel machine learning architecture - we learn this relationship across a broad range of interaction strengths with near-perfect predictive accuracy. Furthermore, we propose a simple analytical binary-entropy-like expression that quantitatively captures the observed correlation for fixed parameters. Our findings open new avenues for characterizing quantum correlations in transport phenomena and provide a powerful framework for predicting entanglement evolution in quantum systems.