Neural Networks for Detecting Multimode Wigner Negativity

The characterization of quantum features in large Hilbert spaces is a crucial requirement for testing quantum protocols. In the continuous variable encoding, quantum homodyne tomography requires an amount of measurement that increases exponentially with the number of involved modes, which practically makes the protocol intractable even with few modes. Here, we introduce a new technique, based on a machine learning protocol with artificial neural networks, that allows us to directly detect negativity of the Wigner function for multimode quantum states. We test the procedure on a whole class of numerically simulated multimode quantum states for which the Wigner function is known analytically. We demonstrate that the method is fast, accurate, and more robust than conventional methods when limited amounts of data are available. Moreover, the method is applied to an experimental multimodc quantum state, for which an additional test of resilience to losses is carried out.