Machine learning-aided direct estimation of coherence and entanglement for unknown states

TL;DR

This paper introduces a machine learning method using support vector regression to efficiently estimate quantum coherence and entanglement from minimal experimental data, reducing resource needs in high-dimensional quantum systems.

Contribution

The paper presents a novel SVR-based approach that directly estimates quantum resources using limited measurements, improving efficiency over traditional quantum state tomography.

Findings

Achieves over 95% conservative lower bounds in predictions.

Requires only diagonal and trace measurements, reducing experimental resources.

Maintains high accuracy despite input perturbations.

Abstract

Quantum coherence and entanglement are fundamental resources in quantum technologies, yet their efficient estimation for unknown states by employing minimal resources in experimental settings remains challenging, particularly in high-dimensional systems. We present a machine learning approach based on support vector regression (SVR) that directly estimates the coherence measures and the geometric measure of quantum entanglement using minimal experimental resources. Our method requires only the diagonal entries of the density matrix, along with the traces of the squared and cubed density matrices for quantum coherence, and additionally along with the traces of the squared and cubed reduced density matrix for estimating quantum entanglement. These quantities can be obtained through random measurements or a hybrid quantum-classical framework. This approach significantly reduces the resource overhead compared to quantum state tomography while maintaining high accuracy. {Furthermore, the support vector quantile regression (SVQR) with pinball loss is employed to prevent SVR overestimation. This model not only ensures that over 95\% of predictions are conservative lower bounds in most cases, but also maintains this lower-bound reliability for over 93\% of predictions, despite 2\% perturbations in the input features.} The proposed technique provides a practical and scalable tool for characterizing quantum resources across computation, communication, and metrology applications.