  We study quasi-two-dimensional dipolar Bose-Einstein condensates, in which
the Bogoliubov excitation spectrum displays, at sufficiently large gas density,
a deep roton minimum due to the spatially anisotropic behavior of the dipolar
two-body potential. A rapid quench, performed on the speed of sound of
excitations propagating on the condensate background, leads to the dynamical
Casimir effect, which can be characterized by measuring the density-density
correlation function. It is shown, for both zero and finite initial
temperatures, that the continuous-variable bipartite quantum state of the
created quasiparticle pairs with opposite momenta, resulting from the quench,
displays an enhanced potential for the presence of entanglement (represented by
nonseparable and steerable quasiparticle states), when compared to a gas with
solely repulsive contact interactions. Steerable quasiparticle pairs contain
momenta from close to the roton, and hence quantum correlations significantly
increase in the presence of a deep roton minimum.
