  Creation of correlated photon pairs is one of the key topics in contemporary
quantum optics. Here, we theoretically describe the generation of photon pairs
in the process of spontaneous parametric down-conversion in a resonant
spherical nanoparticle made of a dielectric material with bulk $\chi^{(2)}$
nonlinearity. We pick the nanoparticle size that satisfies the condition of
resonant eigenmodes described by Mie theory. We reveal that highly directional
photon-pair generation can be observed utilising the nonlinear Kerker-type
effect, and that this regime provides useful polarisation correlations.
