  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
|\psi > =|dyon+> |scalar-> +/- |dyon->|scalar+>. We determine the energy levels
and the wave functions and also discuss their stability.
