  Photon antibunching is a quantum phenomenon typically observed in strongly
nonlinear systems where photon blockade suppresses the probability for
detecting two photons at the same time. Antibunching has also been reported
with Gaussian states, where optimized amplitude squeezing yields classically
forbidden values of the intensity correlation, $g^{(2)}(0)<1$. As a
consequence, observing antibunching is not necessarily a signature of
photon-photon interactions. To clarify the significance of the intensity
correlations, we derive a sufficient condition for deducing if a field is
non-Gaussian based on a $g^{(2)}(0)$ measurement. We then show that the
Gaussian antibunching obtained with a degenerate parametric amplifier is close
to the ideal case reached using dissipative squeezing protocols. We finally
shed light on the so-called unconventional photon blockade effect predicted in
a driven two-cavity setup with surprisingly weak Kerr nonlinearities, stressing
that it is a particular realization of optimized Gaussian amplitude squeezing.
