The whole is greater than the sum of the parts: on the possibility of purely statistical interpretations of quantum theory

Abstract

The Pusey-Barrett-Rudolph theorem (PBR) claims to rule out the possibility of a purely statistical interpretation of the quantum state under an assumption of how to represent independent operations in any hidden variable model. We show that PBR's assumption of independence encodes an assumption of local causality, which is already known to conflict with the predictions of quantum theory via Bell-type inequalities. We devise a weaker formulation of independence within a general hidden variable model that is empirically indistinguishable from the PBR assumption in situations where certain hidden variables are inaccessible. Under this weaker principle we are able to construct an explicit hidden variable model that is purely statistical and also reproduces the quantum predictions. Our results suggest that the assumption of a purely statistical interpretation is actually an innocent bystander in the PBR argument, rather than the driving force behind their contradiction.

5 + epsilon pages. Comments welcome

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