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

Directional correlations in quantum walks with two particles