  We consider a generation of two-particle quantum states in the process of
spontaneous parametric down-conversion of light by a dielectric nanoparticle
with $\chi^{(2)}$ response. As a particular example, we study the generation of
surface plasmon-polariton pairs with a ${\rm GaAs}$ nanoparticle located at the
silver-air interface. We show that for certain excitation geometries, ${\rm
N00N}$-states of surface plasmon-polariton pairs could be obtained. The effect
can be physically interpreted as a result of quantum interference between pairs
of induced sources, each emitting either signal or idler plasmon. We then
relate the resulting ${\rm N00N}$-pattern to the general symmetry properties of
dyadic Green's function of a dipole emitter exciting surface waves. It renders
the considered effect as a general way towards a robust generation of ${\rm
N00N}$-states of surface waves using spontaneous parametric down-conversion in
$\chi^{(2)}$ nanoparticles.
