Failure of epistemic models to explain the antidistinguishability of quantum mixed preparations

We investigate the limits of epistemic models in reproducing the empirical predictions of general quantum preparations. This involves comparing the common quantum overlap determined by the anti-distinguishability of a set of preparations with the common epistemic overlap of the probability distribution over the ontic states describing these preparations. We show that no epistemic model with non-zero common overlap can reproduce the predictions of quantum theory for mixed preparations, even for qubit systems. We explicitly provide sets of distinct mixed preparations, starting from qutrit systems, that give rise to identical quantum mixed states for which the common epistemic overlap must be zero. Finally, we demonstrate the strongest form of preparation contextuality by presenting pairs of mixed preparations that yield identical quantum mixed states while their epistemic overlap must vanish.