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 \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 $|\psi ⟩,|\varphi ⟩$ could be ontologically indistinct (there are ontological states which fail to distinguish between these quantum states). A similar method proves that if $|⟨\varphi |\psi ⟩{|}^2\in (0,\frac{1}{4})$ then $|\psi ⟩,|\varphi ⟩$ must approach ontological distinctness as $d\to \infty$. The robustness of these results to small experimental error is also discussed.

Updated to published version with slgihtly extended discussion and corrected mistakes. 6 + 7 pages, Quantum Studies: Mathematics and Foundations. Online First. (2015)

References in corpus (2)

• Is the quantum state real? An extended review of $\psi$-ontology theorems
• How ψ-epistemic models fail at explaining the indistinguishability of quantum states

Cited by in corpus (4)

• Quantum Advantage from Sequential-Transformation Contextuality
• Reality of the quantum state: Towards a stronger ψ-ontology theorem
• A Stronger Theorem Against Macro-realism
• Constraints on Macroscopic Realism Without Assuming Non-Invasive Measurability