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

Understand

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.