  In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a
transition to chaos when its tunnelling rate is modulated in time. We use exact
and approximate numerical simulations to determine the features of the
dynamically evolving state that are correlated with the presence of chaos in
the classical limit. We propose the statistical distance between initially
similar number distributions as a reliable measure to distinguish regular from
chaotic behaviour in the quantum dynamics. Besides being experimentally
accessible, number distributions can be efficiently reconstructed numerically
from binned phase-space trajectories in a truncated Wigner approximation.
Although the evolving Wigner function becomes very irregular in the chaotic
regions, the truncated Wigner method is nevertheless able to capture accurately
the beyond mean-field dynamics.
