  Quantum walks on the line with a single particle possess a classical analog.
Involving more walkers opens up the possibility to study collective quantum
effects, such as many particle correlations. In this context, entangled initial
states and indistinguishability of the particles play a role. We consider
directional correlations between two particles performing a quantum walk on a
line. For non-interacting particles we find analytic asymptotic expressions and
give the limits of directional correlations. We show that introducing
$\delta$-interaction between the particles, one can exceed the limits for
non-interacting particles.
