Transforming Bell’s inequalities into state classifiers with machine learning

Abstract

In quantum information science, a major challenge is to look for an efficient means for classifying quantum states. An attractive proposal is to utilize Bell’s inequality as an entanglement witness, for classifying entangled state. The problem is that entanglement is necessary but not sufficient for violating Bell’s inequalities, making these inequalities unreliable in state classification. Furthermore, in general, classifying the separability of states, even for only few qubits, is resource-consuming. Here we look for alternative solutions with the methods of machine learning, by constructing neural networks that are capable of simultaneously encoding convex sets of multiple entanglement witness inequalities. The simulation results indicated that these transformed Bell-type classifiers can perform significantly better than the original Bell’s inequalities in classifying entangled states. We further extended our analysis to classify quantum states into multiple species through machine learning. These results not only provide an interpretation of neural network as quantum state classifier, but also confirm that neural networks can be a valuable tool for quantum information processing.