Machine Learning for Detecting Steering in Qutrit-Pair States

TL;DR

This paper develops machine learning models, trained on a rigorously labeled dataset created via semidefinite programming, to detect steerability in high-dimensional qutrit-qutrit quantum states, achieving high accuracy and revealing new steerable states.

Contribution

It introduces the first rigorously labeled dataset for steerability detection in qutrit systems and demonstrates the effectiveness of neural networks with engineered features in this task.

Findings

Neural networks outperform support vector machines in steerability classification.

Feature engineering with a steering ellipsoid-like feature improves model performance.

The models successfully identify new steerable states and boundaries in high-dimensional systems.

Abstract

Only a few states in high-dimensional systems can be identified as (un)steerable using existing theoretical or experimental methods. We utilize semidefinite programming (SDP) to construct a dataset for steerability detection in qutrit-qutrit systems. For the full-information feature $F_1$, artificial neural networks achieve high classification accuracy and generalization, and preform better than the support vector machine. As feature engineering playing a pivotal role, we introduce a steering ellipsoid-like feature $F_2$, which significantly enhances the performance of each of our models. Given the SDP method provides only a sufficient condition for steerability detection, we establish the first rigorously constructed, accurately labeled dataset based on theoretical foundations. This dataset enables models to exhibit outstanding accuracy and generalization capabilities, independent of the choice of features. As applications, we investigate the steerability boundaries of isotropic states and partially entangled states, and find new steerable states. This work not only advances the application of machine learning for probing quantum steerability in high-dimensional systems but also deepens the theoretical understanding of quantum steerability itself.