Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomena

TL;DR

This paper extends the Pusey-Barrett-Rudolph theorem by weakening its assumptions, notably replacing factorisability with a less restrictive compatibility condition and removing measurement independence, thus broadening the scope of models constrained.

Contribution

It generalizes the PBR theorem by introducing weaker assumptions, avoiding reductionism, and demonstrating similar restrictions on quantum models under less stringent conditions.

Findings

Weakened assumptions still restrict quantum models effectively.

Compatibility replaces factorisability in the theorem.

Measurement independence can be omitted without losing the result.

Abstract

Pusey, Barrett and Rudolph (PBR) have recently given a completely novel argument that restricts the class of possible models for quantum phenomena (arXiv:1111.3328). In these notes the assumptions used by PBR are considerably weakened, to further restrict the class of possible models. The `factorisability' assumption used by PBR is replaced by a far weaker `compatibility' assumption for uncorrelated quantum subsystems which, moreover, does not require the assignation of separate underlying properties to each subsystem (i.e, reductionism). Further, it is shown that an assumption of measurement independence may be dropped to obtain a related result having the same experimental significance (at the expense of a weaker conceptual significance). The latter is a remarkable feature of the PBR approach, given that Bell inequalities, steering inequalities and Kochen-Specker theorems all require an assumption of this type.