On the Correction of Anomalous Phase Oscillation in Entanglement Witnesses Using Quantum Neural Networks

Entanglement of a quantum system depends upon the relative phase in complicated ways, which no single measurement can reflect. Because of this, “entanglement witnesses” (measures that estimate entanglement) are necessarily limited in applicability and/or utility. We propose here a solution to the problem using quantum neural networks. A quantum system contains the information of its entanglement; thus, if we are clever, we can extract that information efficiently. As proof of concept, we show how this can be done for the case of pure states of a two-qubit system, using an entanglement indicator corrected for the anomalous phase oscillation. Both the entanglement indicator and the phase correction are calculated by the quantum system itself acting as a neural network.