Quantum superpositions cannot be epistemic

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 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 | ψ⟩ , | ϕ⟩ could be ontologically indistinct (there are ontological states which fail to distinguish between these quantum states). A similar method proves that if |⟨ϕ|ψ⟩|2∈(0,14), then | ψ⟩ , | ϕ⟩ must approach ontological distinctness as d→ ∞. The robustness of these results to small experimental error is also discussed.