  Although non-commutativity of a certain set of quantum operators (e.g.,
creation/annihilation operators and Pauli spin operators) has been shown
experimentally in recent years, the commu- tation relation for the position and
the momentum operators has not been directly demonstrated to date. In this
paper, we propose and analyze an experimental scheme for directly observing the
non-commutativity of the position and the momentum operators using
single-photon quantum in- terference. While the scheme is studied for the
single-photon state as the input quantum state, the analysis applies equally to
matter-wave interference, allowing a direct test of the position-momentum
commutation relation with a massive particle.
