The PBR theorem is a theorem about the physical reality of quantum states due to Matthew Pusey, Jonathan Barrett, and Terry Rudolph, named after the initial letters of their surnames.
The theorem was first published as an arXiv preprint, with a subsequent version published in Nature Physics. The theorem states that either the quantum state corresponds to a physically real object and is not merely a statistical tool, or else all quantum states, including non-entangled ones, can communicate by action at a distance. This preliminary result has been referred to as Pusey's theorem or the PBR theorem, and has been cited by theoretical physicist Antony Valentini as "the most important general theorem relating to the foundations of quantum mechanics since Bell's theorem". A revised version was released on 7 May 2012.
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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