  We consider two identical bosons propagating on a one-dimensional lattice and
address the prob- lem of discriminating whether their mutual on-site
interaction is attractive or repulsive. We suggest a probing scheme based on
the properties of the corresponding two-particle quantum walks, and show that
the sign of the interaction introduces specific and detectable features in the
dynamics of quantum correlations, thus permitting to discriminate between the
two cases. We also discuss how these features are connected to the
band-structure of the Hubbard Hamiltonian, and prove that discrimination may be
obtained only when the two walkers are initially prepared in a superposition of
localized states.
