Abstract
The Bell-Kochen-Specker theorem establishes the impossibility of a noncontextual hidden variable model of quantum theory, or equivalently, that quantum theory is contextual. In this paper, an operational definition of contextuality is introduced which generalizes the standard notion in three ways: (i) it applies to arbitrary operational theories rather than just quantum theory, (ii) it applies to arbitrary experimental procedures rather than just sharp measurements, and (iii) it applies to a broad class of ontological models of quantum theory rather than just deterministic hidden variable models. We derive three no-go theorems for ontological models, each based on an assumption of noncontextuality for a different sort of experimental procedure; one for preparation procedures, another for unsharp measurement procedures (that is, measurement procedures associated with positive-operator valued measures), and a third for transformation procedures. All three proofs apply to two-dimensional Hilbert spaces, and are therefore stronger than traditional proofs of contextuality.
- Received 6 September 2004
DOI:https://doi.org/10.1103/PhysRevA.71.052108
©2005 American Physical Society
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Physical Review A 50th Anniversary Milestones
The collection contains papers that have made important contributions to atomic, molecular, and optical physics and quantum information by announcing significant discoveries or by initiating new areas of research.