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 Greens 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.
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