Distinguishing initial state-vectors from each other in histories formulations and the PBR argument

Abstract: Following the argument of Pusey, Barrett and Rudolph (Nature Phys. 8:476, 2012), new interest has been raised on whether one can interpret state-vectors (pure states) in a statistical way ($\psi$-epistemic theories), or if each of them corresponds to a different ontological entity. Each interpretation of quantum theory assumes different ontology and one could ask if the PBR argument carries over. Here we examine this question for histories formulations in general with particular attention to the co-event formulation. State-vectors appear as the initial state that enters into the quantum measure. While the PBR argument goes through up to a point, the failure to meet some of the assumptions they made does not allow one to reach their conclusion. However, the author believes that the "statistical interpretation" is still impossible for co-events even if this is not proven by the PBR argument.