Transforming Bell's Inequalities into State Classifiers with Machine Learning

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. A new approach combines machine-learning techniques with Bell’s inequality for efficient entanglement detection. Classifying entangled states is a computationally demanding task. Of particular relevance for quantum information processing tasks is the distinction between entangled and separable states. Although Bell’s inequality can be violated only by entangled states, it isn’t a reliable entanglement witness. In fact, for each form of the inequality some entangled states won’t lead to any violation. Yue-Chi Ma and Man-Hong Yung from China’s Tsinghua University have now shown that a suitably trained artificial neural network can find the optimal form of Bell’s inequality to efficiently determine if an unknown bipartite or tripartite state is entangled or separable. Beyond entanglement detection, this optimisation approach could be used to construct optimal operators for other quantum state classification tasks.

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