We show that the presence of finite-size monopoles can lead to a number of interesting physical processes involving quantum entanglement of charges. Taking as a model the classical solution of the N = 2 SU(2) Yang-Mills theory, we study interaction between dyons and scalar particles in the adjoint and fundamental representation. We find that there are bound states of scalars and dyons, which, remarkably, are always an entangled configuration of the form vertical bar psi> = verical bar dyon(+)i>vertical bar scalar_>+/- vertical bar dyon_>vertical bar scalar(+)>. We determine the energy levels and the wave functions and also discuss their stability.
