Universal learning of nonlocal entropy via local correlations in non-equilibrium quantum states

TL;DR

This paper introduces a machine learning method to infer nonlocal quantum information, specifically quantum mutual information, from local measurements in nonequilibrium quantum states, facilitating experimental studies.

Contribution

It presents a universal neural network-based approach to map local correlations to nonlocal quantum mutual information in nonequilibrium states.

Findings

Successfully maps local correlations to QMI in disordered XXZ model

Enables experimental extraction of QMI in quantum platforms

Framework applicable to other nonlocal observables like Fisher information

Abstract

Characterizing the nonlocal nature of quantum states is a central challenge in the practical application of large-scale quantum computation and simulation. Quantum mutual information (QMI), a fundamental nonlocal measure, plays a key role in quantifying entanglement and has become increasingly important in studying nonequilibrium quantum many-body phenomena, such as many-body localization and thermalization. However, experimental measurement of QMI remains extremely difficult, particularly for nonequilibrium states, which are more complex than ground states. In this Letter, we employ a multilayer perceptron (MLP) to establish a universal mapping between the QMI and local correlations only up to second order for nonequilibrium states generated by quenches in a one-dimensional disordered XXZ model. Our approach provides a practical method for experimentally extracting QMI, readily applicable in platforms such as superconducting qubits. Moreover, this work will establishes a general framework for reconstructing other nonlocal observables, including Fisher information and out-of-time-ordered correlators.