  The dynamics of a particle propagating in free space is described by its
position and momentum, where quantum mechanics prohibits the simultaneous
identification of two non-commutative physical quantities. Recently, a lower
bound on the probability of finding a particle after propagating for a given
time has been derived for well-defined initial constraints on position and
momentum under the assumption that particles travel in straight lines. Here, we
investigate this lower limit experimentally with photons. We prepared a
superposition of position and momentum states by using slits, lenses and an
interferometer, and observed a quantum interference between position and
momentum. The lower bound was then evaluated using the initial state and the
result was 5.9\% below this classical bound.
