  We study the effect of interactions on the bosonic two-particle quantum walk
and its corresponding spatial correlations. The combined effect of interactions
and Hanbury-Brown Twiss interference results in unique spatial correlations
which depend on the strength of the interaction, but not on its sign. The
results are explained in light of the two-particle spectrum and the physics of
attractively and repulsively bound pairs. We experimentally measure the weak
interaction limit of these effects in nonlinear photonic lattices. Finally, we
discuss an experimental approach to observe the strong interaction limit using
single atoms in optical lattices.
