This paper proposes groovelike potential structures for the observation of quantum information processing by trapped particles. As an illustration the effect of quantum statistics at a 50-50 beam splitter is investigated. For noninteracting particles we regain the results known from photon experiments, but we have found that particle interactions destroy the perfect bosonic correlations. Fermions avoid each other due to the exclusion principle and hence they are far less sensitive to particle interactions. For bosons, the behavior can be explained with simple analytic considerations which predict a certain amount of universality. This is verified by detailed numerical calculations. [S1050-2937(99)03205-9].