Reflections on the PBR Theorem: Reality Criteria & Preparation Independence

TL;DR

This paper re-examines the PBR theorem by refining reality criteria for the wavefunction, analyzing preparation independence, and proposing a weaker assumption akin to no-signalling, leading to new insights on non-locality and contextuality.

Contribution

It introduces a dualized reality criterion for the wavefunction and proposes a weakened preparation independence assumption, expanding the foundational understanding of quantum non-locality.

Findings

A new criterion for wavefunction reality avoiding measure-zero issues

A formal analogy between preparation independence and Bell locality

Counter-example violating PBR but satisfying the relaxed assumption

Abstract

This paper contains initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves dualising a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the Pusey-Barrett-Rudolph theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable properties of any ontological physical theory a new characterisation of non-locality and contextuality is found. Secondly, a careful analysis of preparation independence, one of the key assumptions of the PBR theorem, leads to a precise analogy with the kind of locality prohibited by Bell's theorem. Motivated by this, we propose a weakening of the assumption to something analogous to no-signalling. This amounts to allowing global or non-local correlations in the joint ontic state, which nevertheless do not allow for superluminal signalling. This is, at least, consistent with the Bell and Kochen-Specker theorems. We find a counter-example to the PBR argument, which violates preparation independence, but does satisfy this physically motivated assumption. The question of whether the PBR result can be strengthened to hold under the relaxed assumption is therefore posed.