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

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.

Figure 1

Existence or nonexistence of nontrivial epistemic overlaps for distributions induced by pairs of distinct, pure quantum states characterize (a) $\psi$-epistemic and (b) $\psi$-ontic ontological theories, respectively. The term epistemic overlap is made precise in Eq. (2).

Figure 2

(a) Spatially separated, preparation-independent devices. (b) A classical-correlation scenario in which correlations may be mediated through a common past. (c) Dashed lines represent correlations forbidden by the subsystem condition.