  Despite being the most fundamental object in quantum theory, physicists are
yet to reach a consensus on the interpretation of a quantum wavefunction. In
the broad class of realist approaches, quantum states are viewed as
Liouville-like probability distributions over some space of physical variables
where indistinguishabity of non-orthogonal states is attributed to overlaps
between these distributions. Here we argue that such an interpretation of
quantum indistinguishability is wrong. In particular, we show that quantum
mechanical prediction of maximal violation of Mermin inequality in certain
thought experiment is incompatible with all ontological interpretations for
quantum theory where indistinguishability of non-orthonal quantum states is
explained, even partially, in terms of overlap of their Liouville
distributions.
