The status of the quantum state is perhaps the most controversial
issue in the foundations of quantum theory. Is it an epistemic state
(representing knowledge, information, or belief) or an ontic state (a
direct reflection of reality)? In the ontological models framework,
quantum states correspond to probability measures over more
fundamental states of reality. The quantum state is then ontic if
every pair of pure states corresponds to a pair of measures that do
not overlap, and is otherwise epistemic. Recently, several authors
have derived theorems that aim to show that the quantum state must be
ontic in this framework. Each of these theorems involve auxiliary
assumptions of varying degrees of plausibility. Without such
assumptions, it has been shown that models exist in which the quantum
state is epistemic. However, the definition of an epistemic quantum
state used in these works is extremely permissive. Only two quantum
states need correspond to overlapping measures and furthermore the
amount of overlap may be arbitrarily small. In order to provide an
explanation of quantum phenomena such as no-cloning and the
indistinguishability of pure states, the amount of overlap should be
comparable to the inner product of the quantum states. In this talk, I
review the debate over the interpretation of quantum states and
explain how the overlap of probability measures can be bounded using
proofs of the Kochen-Specker theorem. In particular, I exhibit a
family of states in d-dimensional Hilbert space for which the ratio of
overlap to inner product must be ≤ de^{-cd} for some positive
constant c, which severely constrains the epistemic interpretation of
quantum states.