Reality of the quantum state: Towards a stronger {\psi}-ontology theorem

TL;DR

This paper explores weaker assumptions than the original PBR theorem to argue for the reality of the quantum state, demonstrating that the theorem's conclusions do not hold under these more physically realistic conditions.

Contribution

It introduces less restrictive notions of independence in the PBR framework and derives a new theorem supporting the reality of the quantum state under these conditions.

Findings

The PBR argument fails under weaker independence assumptions.

A new bound on {}-epistemicity consistent with quantum predictions.

The approximation becomes exact with infinitely many preparations.

Abstract

The Pusey-Barrett-Rudolph (PBR) no-go theorem provides an argument for the reality of the quantum state by ruling out {\psi}-epistemic ontological theories, in which the quantum state is of a statistical nature. It applies under an assumption of preparation independence, the validity of which has been subject to debate. We propose two plausible and less restrictive alternatives: a weaker notion allowing for classical correlations, and an even weaker, physically motivated notion of independence, which merely prohibits the possibility of superluminal causal influences in the preparation process. The latter is a minimal requirement for enabling a reasonable treatment of subsystems in any theory. It is demonstrated by means of an explicit {\psi}-epistemic ontological model that the argument of PBR becomes invalid under the alternative notions of independence. As an intermediate step, we recover a result which is valid in the presence of classical correlations. Finally, we obtain a theorem which holds under the minimal requirement, approximating the result of PBR. For this, we consider experiments involving randomly sampled preparations and derive bounds on the degree of {\psi} epistemicity that is consistent with the quantum-mechanical predictions. The approximation is exact in the limit as the sample space of preparations becomes infinite.