Estimating classical mutual information between quantum subsystems with neural networks

TL;DR

This paper demonstrates that neural networks can reliably estimate classical mutual information and entropy in quantum systems from limited measurements, aiding phase diagram reconstruction.

Contribution

It introduces a neural network method to estimate mutual information in quantum systems using limited projective measurements, reducing the need for complete state statistics.

Findings

Neural networks accurately estimate mutual information in quantum states.

The approach works well even for delocalized paramagnetic wave functions.

The phase diagram of the quantum Ising model is successfully reconstructed.

Abstract

Characterizing correlations in a quantum system on the basis of the results of the projective measurements can be performed with different means including the calculation of the classical mutual information. Generally, estimating such information-entropy-based quantities requires having complete statistics of the system's states. Here we explore the possibility to reconstruct the classical mutual information and specific entropy of a quantum system with neural network approach on the basis of limited number of projective measurements. As a prominent example we consider the antiferromagnetic quantum Ising model in transverse and longitudinal magnetic fields which is in demand in both condensed matter physics and quantum computing. We show that the neural network approach gives reliable estimates of the classical mutual information even in the case of paramagnetic wave functions delocalized in the state space. In addition, the phase diagram of the considered quantum system is reconstructed with a special focus on discriminating various types of disordered states.