The PBR theorem is a no-go theorem in quantum foundations due to Matthew Pusey, Jonathan Barrett, and Terry Rudolph (for whom the theorem is named). It has particular significance for how one may interpret the nature of the quantum state.
With respect to certain realist hidden variable theories that attempt to explain the predictions of quantum mechanics, the theorem rules that pure quantum states must be "ontic" in the sense that they correspond directly to states of reality, rather than "epistemic" in the sense that they represents probabilistic or incomplete states of knowledge about reality.
The PBR theorem may also be compared with other no-go theorems like Bell's theorem and the Bell–Kochen–Specker theorem, which, respectively, rule out the possibility of explaining the predictions of quantum mechanics with local hidden variable theories and noncontextual hidden variable theories. Similarly, the PBR theorem could be said to rule out preparation independent hidden variable theories, in which quantum states that are prepared independently have independent hidden variable descriptions.
This theorem, which first appeared as an arXiv preprint and was subsequently published in Nature Physics, concerns the interpretational status of pure quantum states. Under the classification of hidden variable models of Harrigan and Spekkens, the interpretation of the quantum wavefunction can be categorized as either ψ-ontic if "every complete physical state ontic state in the theory is consistent with only one pure quantum state" and ψ-epistemic "if there exist ontic states that are consistent with more than one pure quantum state." The PBR theorem proves that either the quantum state is ψ-ontic, or else non-entangled quantum states violate the assumption of preparation independence, which would entail action at a distance.
In conclusion, we have presented a no-go theorem, which - modulo assumptions - shows that models in which the quantum state is interpreted as mere information about an objective physical state of a system cannot reproduce the predictions of quantum theory. The result is in the same spirit as Bell’s theorem, which states that no local theory can reproduce the predictions of quantum theory.— Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph, "On the reality of the quantum state", Nature Physics 8, 475-478 (2012)
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