  Non-Gaussian correlations in a pure state are inextricably linked with
non-classical features, such as a non positive-definite Wigner function. In a
commonly used simulation technique in ultracold atoms and quantum optics, known
as the truncated Wigner method, the quantum dynamics is mapped to stochastic
trajectories in phase space, governed by a positive approximation to the true
Wigner distribution. The question thus arises: how accurate is this approach in
predicting truly non-classical behaviour? In this article, we benchmark the
ability of the truncated Wigner phase-space method to reproduce the
non-Gaussian statistics of the single mode anharmonic oscillator. We find that
the this method can reliably predict departures from Gaussian statistics over a
wide range of particle numbers, whereas the positive-P representation method,
which is in principle exact, can suffer from divergent instabilities. The
truncated Wigner function, furthermore, is able to reproduce the non-Gaussian
correlations while satisfying the condition for purity.
