Transforming Bell's Inequalities into State Classifiers with Machine Learning

TL;DR

This paper uses machine learning to transform Bell's inequalities into effective quantum state classifiers, improving entanglement detection with partial information across multi-qubit systems.

Contribution

The study introduces a machine learning approach to enhance Bell's inequalities as reliable classifiers for quantum entanglement detection.

Findings

Transformed Bell-type inequalities outperform original ones in classifying entangled states.

Machine learning enables effective classification with partial quantum state information.

Extended analysis successfully classifies multi-qubit states into multiple categories.

Abstract

Quantum information science has profoundly changed the ways we understand, store, and process information. A major challenge in this field is to look for an efficient means for classifying quantum state. For instance, one may want to determine if a given quantum state is entangled or not. However, the process of a complete characterization of quantum states, known as quantum state tomography, is a resource-consuming operation in general. An attractive proposal would be the use of Bell's inequalities as an entanglement witness, where only partial information of the quantum state is needed. The problem is that entanglement is necessary but not sufficient for violating Bell's inequalities, making it an unreliable state classifier. Here we aim at solving this problem by the methods of machine learning. More precisely, given a family of quantum states, we randomly picked a subset of it to construct a quantum-state classifier, accepting only partial information of each quantum state. Our results indicated that these transformed Bell-type inequalities can perform significantly better than the original Bell's inequalities in classifying entangled states. We further extended our analysis to three-qubit and four-qubit systems, performing classification of quantum states into multiple species. These results demonstrate how the tools in machine learning can be applied to solving problems in quantum information science.