  The characterization of quantum features in large Hilbert spaces is a crucial
requirement for testing quantum protocols. In the continuous variables
encoding, quantum homodyne tomography requires an amount of measurements 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 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 multimode quantum state, for which an
additional test of resilience to losses is carried out.
