  The status of the quantum state is perhaps the most controversial issue in
the foundations of quantum theory. Is it an epistemic state (state of
knowledge) or an ontic state (state of reality)? In realist models of quantum
theory, the epistemic view asserts that nonorthogonal quantum states correspond
to overlapping probability measures over the true ontic states. This naturally
accounts for a large number of otherwise puzzling quantum phenomena. For
example, the indistinguishability of nonorthogonal states is explained by the
fact that the ontic state sometimes lies in the overlap region, in which case
there is nothing in reality that could distinguish the two states. For this to
work, the amount of overlap of the probability measures should be comparable to
the indistinguishability of the quantum states. In this letter, I exhibit a
family of states for which the ratio of these two quantities must be $\leq
2de^{-cd}$ in Hilbert spaces of dimension $d$ that are divisible by $4$. This
implies that, for large Hilbert space dimension, the epistemic explanation of
indistinguishability becomes implausible at an exponential rate as the Hilbert
space dimension increases.
