  We investigate the impact of non-Gaussian lensing deflections on measurements
of the CMB lensing power spectrum. We find that the false assumption of their
Gaussianity significantly biases these measurements in current and future
experiments at the percent level. The bias is detected by comparing CMB lensing
reconstructions from simulated CMB data lensed with Gaussian deflection fields
to reconstructions from simulations lensed with fully non-Gaussian deflection
fields. The non-Gaussian deflections are produced by ray-tracing through
snapshots of an N-body simulation and capture both the non-Gaussianity induced
by non-linear structure formation and by multiple correlated deflections. We
find that the amplitude of the measured bias is in agreement with analytical
predictions by B\"ohm et al. 2016. The bias is largest in temperature-based
measurements and we do not find evidence for it in measurements from a
combination of polarization fields ($EB,EB$). We argue that the non-Gaussian
bias should be even more important for measurements of cross-correlations of
CMB lensing with low-redshift tracers of large-scale structure.
