| Pusey–Barrett–Rudolph theorem | |
|---|---|
| Name | Pusey–Barrett–Rudolph theorem |
| Field | Quantum foundations |
| Statement | Quantum states correspond to physical reality under specified assumptions |
| Year | 2012 |
| Authors | Matthew F. Pusey; Jonathan Barrett; Terry Rudolph |
| Related | Bell's theorem; Kochen–Specker theorem; ψ-ontology theorems |
Pusey–Barrett–Rudolph theorem
The Pusey–Barrett–Rudolph theorem (often abbreviated PBR) is a result in the foundations of quantum mechanics which argues that, given plausible assumptions, distinct quantum states must correspond to distinct physical realities rather than merely representing information about an underlying state of affairs. The theorem constrains classes of ontic and epistemic interpretations of the quantum state and has stimulated extensive follow-up work, experimental tests, and philosophical debate within the community studying quantum foundations.
The PBR theorem, published by Matthew F. Pusey, Jonathan Barrett and Terry Rudolph in 2012, formalizes a no-go result for certain models in which the wave function (or quantum state) is treated as purely epistemic. Under two main assumptions—preparation independence and the standard quantum predictions—the theorem shows that the probability distributions over hypothetical underlying physical states (so-called ontic states) assigned to different pure quantum states must have disjoint support. In other words, nonorthogonal quantum states cannot correspond to overlapping distributions over the same underlying reality, implying a form of ψ-ontology: the ψ has ontic status.
The PBR theorem fits into a lineage of results probing the status of the quantum state, notably Bell's theorem (1964) which addresses locality and hidden variables, and the Kochen–Specker theorem (1967) which addresses noncontextuality. Prior to PBR, proponents of epistemic accounts—such as models inspired by classical probability or statistical interpretations and works by Spekkens—argued that the quantum state represents knowledge or information rather than reality. PBR responded to this program by providing an argument that rules out a broad class of epistemic models, reviving debates about realism in quantum theory and influencing discussions at institutions like Perimeter Institute for Theoretical Physics and Institute for Quantum Information and Matter.
The theorem is formulated within the framework of ontological models of quantum theory. An ontological model associates with each preparation procedure a probability distribution over an ontic state space Λ, and with each measurement a response function on Λ, reproducing Born probabilities. Key definitions include: - ψ-ontic models: distinct quantum states correspond to non-overlapping distributions on Λ. - ψ-epistemic models: distinct quantum states may correspond to overlapping distributions, allowing the quantum state to represent incomplete knowledge. The PBR argument rests principally on the assumption of preparation independence: independently prepared systems have product distributions on the joint ontic space. It also assumes standard quantum predictions for measurement statistics. These assumptions are debated and connected to concepts like separability and preparation contextuality.
The PBR proof constructs scenarios using multiple independently prepared copies of systems in selected nonorthogonal pure states. By choosing product states and performing entangled measurements on the joint system, the argument identifies a measurement outcome that would be impossible if overlaps between distributions for distinct ψ were allowed, while quantum mechanics predicts a nonzero probability. The proof uses combinatorial lemmas about supports of product distributions and exploits tensor-product structure of composite quantum systems. Central technical steps relate to deriving contradictions between assumed overlaps and the existence of outcome probabilities predicted by specific entangled measurements (often analysed using projective measurements and properties of tensor-product Hilbert spaces).
If the PBR assumptions are accepted, the theorem supports interpretations in which the quantum state has direct physical significance (ψ-ontology). This bears on interpretations such as many-worlds interpretation, certain realist versions of de Broglie–Bohm theory (pilot-wave theory), and objective-collapse proposals like the GRW theory. Conversely, strictly epistemic readings—those akin to classical statistical ensembles—are severely constrained. The result does not by itself decide issues of locality or contextuality addressed by Bell inequalities or Kochen–Specker contextuality, but it interacts with these constraints to narrow the landscape of viable interpretations.
Following PBR, experimental groups proposed and performed tests implementing the required state preparations and measurements with systems such as photonic qubits, trapped ions, and superconducting qubits. Experiments by teams building on techniques from quantum information—using Bell-state measurements, linear optics, and high-fidelity state preparation—have reported results consistent with quantum predictions and placed bounds on allowable overlaps in ontological models. These works often cite practical considerations like imperfect preparation, measurement error, and assumptions required to rule out loopholes analogous to those in Bell test experiments.
Critics have questioned the reasonableness of preparation independence and examined models that evade PBR by relaxing that assumption or allowing retrocausality. Subsequent theoretical work produced variants and strengthenings of ψ-ontology theorems, linking PBR to results by Colbeck and Renner and exploring connections with concepts like preparation contextuality and generalized probabilistic theories. Extensions examine finite-resource versions, robustness to noise, and applicability to mixed states. The debate has also stimulated careful analysis of operational assumptions used in foundational theorems and inspired research into reconstructing quantum theory from informational axioms at institutions such as Oxford University and University of Cambridge.
Category:Quantum foundations Category:Theorems in quantum mechanics