  In spite of the interference manifested in the double-slit experiment,
quantum theory predicts that a measure of interference defined by Sorkin and
involving various outcome probabilities from an experiment with three slits, is
identically zero. We adapt Sorkin's measure into a general operational
probabilistic framework for physical theories, and then study its relationship
to the structure of quantum theory. In particular, we characterize the class of
probabilistic theories for which the interference measure is zero as ones in
which it is possible to fully determine the state of a system via specific sets
of 'two-slit' experiments.
