On the reality of the quantum state once again

The Pusey, Barrett and Rudolph (PBR) theorem claims that quantum states cannot be taken to represent mere information about the system. This result is based on the ontological model framework proposed by Harrigan and Spekkens (HS). In this paper we show that the HS framework has a fundamental problem: the epistemic structure it implicitly assumes does not follow the one dictated by quantum mechanics. Namely, the map between the epistemic states of the model and quantum density matrices preserves neither the value nor ordering of the information entropy. Consequently the epistemic content of mixed states is not mapped in a meaningful way. The problem stems from the assumption that an epistemic state is characterized by a single probability measure, which is essentially an assumption of non-contextuality. Given this fundamental issue, every result that uses the HS framework, including the PBR theorem, should be carefully reexamined