Automated machine learning can classify bound entangled states with tomograms

For quantum systems with total dimension greater than six, the positive partial transposition (PPT) criterion is necessary but not sufficient to decide the non-separability of quantum states. Here, we present an automated machine learning approach to classify random states of two qutrits as separable or entangled even when the PPT criterion fails. We successfully applied our framework using enough data to perform a complete quantum state tomography and without any direct measurement of its entanglement. In addition, we could also estimate the generalized robustness of entanglement with regression techniques and use it to validate our classifiers.

Automated summary

In this study, an automated machine learning approach is proposed for classifying states of two qutrits as separable or entangled, even when the traditional PPT criterion fails. The framework was successfully applied to perform complete quantum state tomography without direct measurement of entanglement, and regression techniques were used to estimate the generalized robustness of entanglement and validate the classifiers.