ThePusey–Barrett–Rudolph (PBR)theorem[1] is ano-go theorem inquantum foundations due to Matthew Pusey, Jonathan Barrett, andTerry Rudolph (for whom the theorem is named) in 2012. It has particular significance for how one may interpret the nature of thequantum state.
With respect to certain realisthidden variable theories that attempt to explain the predictions ofquantum 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 represent probabilistic or incomplete states of knowledge about reality.
The PBR theorem may also be compared with other no-go theorems likeBell's theorem and theBell–Kochen–Specker theorem, which, respectively, rule out the possibility of explaining the predictions of quantum mechanics withlocal hidden variable theories and noncontextual hidden variable theories. Similarly, the PBR theorem could be said to rule outpreparation independent hidden variable theories, in which quantum states that are prepared independently have independent hidden variable descriptions.
This result was cited by theoretical physicistAntony Valentini as "the most important general theorem relating to the foundations of quantum mechanics sinceBell's theorem".[2]
This theorem, which first appeared as anarXiv preprint[3] and was subsequently published inNature Physics,[1] concerns the interpretational status of pure quantum states. Under the classification of hidden variable models of Harrigan and Spekkens,[4] the interpretation of the quantum wavefunction can be categorized as eitherψ-ontic if "every complete physical state or ontic state in the theory is consistent with only one pure quantum state" andψ-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 isψ-ontic, or else non-entangled quantum states violate the assumption of preparation independence, which would entailaction at a distance.
In conclusion, we have presented ano-go theorem, which—modulo assumptions—shows that models in which the quantum state is interpreted as mereinformation 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 Physics8, 475-478 (2012)
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