  Perhaps the quantum state represents information about reality, and not
reality directly. Wave function collapse is then possibly no more mysterious
than a Bayesian update of a probability distribution given new data. We
consider models for quantum systems with measurement outcomes determined by an
underlying physical state of the system but where several quantum states are
consistent with a single underlying state---i.e., probability distributions for
distinct quantum states overlap. Significantly, we demonstrate by example that
additional assumptions are always necessary to rule out such a model.
