  Recent experiments have revealed that beyond-mean-field corrections are much
more relevant in weakly-interacting dipolar condensates than in their
non-dipolar counterparts. We show that in quasi-one-dimensional geometries
quantum corrections in dipolar and non-dipolar condensates are strikingly
different due to the peculiar momentum dependence of the dipolar interactions.
The energy correction of the condensate presents not only a modified density
dependence, but it may even change from attractive to repulsive at a critical
density due to the surprising role played by the transversal directions. The
anomalous quantum correction translates into a strongly modified physics for
quantum-stabilized droplets and dipolar solitons. Moreover, and for similar
reasons, quantum corrections of three-body correlations, and hence of
three-body losses, are strongly modified by the dipolar interactions. This
intriguing physics can be readily probed in current experiments with magnetic
atoms.
