  We address the fundamental question of whether epistemic models can reproduce
the empirical predictions of general quantum preparations. This involves
comparing the common quantum overlap determined by the anti-distinguishability
of a set of mixed preparations with the common epistemic overlap of the
probability distribution over the ontic states describing these preparations. A
set of quantum mixed preparations is deemed to be non-epistemic when the
epistemic overlap must be zero while the corresponding quantum overlap remains
non-zero. In its strongest manifestation, a set of mixed quantum preparations
is fully non-epistemic if the epistemic overlap vanishes while the quantum
overlap reaches its maximum value of one. Remarkably, we show that there exist
sets of non-epistemic mixed preparations even in dimension 2, when the overlap
between three mixed preparations is concerned. Moreover, we present quantum
mixed preparations in dimensions 3 and 4 that are fully non-epistemic
concerning the overlap between four and three preparations, respectively. We
also establish a generic upper bound on the average ratio between the epistemic
and quantum overlap for two mixed preparations. Consequently, the ratio for
certain pairs of quantum mixed preparations is shown to be arbitrarily small in
two different instances, signifying they are non-epistemic in one case and
fully non-epistemic in the other. Finally, we delve into some of the remarkable
implications stemming from our findings.
