Quantum Superpositions Cannot be Epistemic

TL;DR

This paper proves that quantum superpositions cannot be purely epistemic for most high-dimensional systems, implying that ontic superposition states are necessary, and it explores the ontological distinguishability of non-orthogonal states.

Contribution

It establishes that quantum superpositions are inherently ontic in high-dimensional systems, challenging epistemic interpretations and advancing understanding of quantum ontology.

Findings

Superpositions cannot be epistemic for systems with dimension greater than 3.

Non-orthogonal states with overlap less than 1/4 become ontologically distinct as dimension increases.

Results are robust to small experimental errors.

Abstract

Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many qualitative properties of quantum superpositions can also be observed in classical probability distributions leading to a suspicion that superpositions may be explicable as probability distributions over less problematic states, that is, a suspicion that superpositions are \emph{epistemic}. Here, it is proved that, for any quantum system of dimension $d>3$, this cannot be the case for almost all superpositions. Equivalently, any underlying ontology must contain ontic superposition states. A related question concerns the more general possibility that some pairs of non-orthogonal quantum states $|\psi\rangle,|\phi\rangle$ could be ontologically indistinct (there are ontological states which fail to distinguish between these quantum states). A similar method proves that if $|\langle\phi|\psi\rangle|^{2}\in(0,\frac{1}{4})$ then $|\psi\rangle,|\phi\rangle$ must approach ontological distinctness as $d\rightarrow\infty$. The robustness of these results to small experimental error is also discussed.