Contextuality for preparations, transformations, and unsharp measurements

By Robert W. Spekkens. 2004

577 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Physical and Theoretical Chemistry, Physiology

View Paper: https://www.semanticscholar.org/paper/7f4b1ba7f6847cc96d09778debde4604059b9045

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Citations in the corpus

Quasi-probability representations of quantum theory with applications to quantum information science (2010, methodology): “An operational theory (Hardy 2001a, Harrigan and Rudolph 2007, Spekkens 2005) is an attempt to mathematically model a real physical experiment.”
Quantum resource theories (2018, background): “In general, contextuality refers to the particular way in which a state is prepared, a transformation arises, or a measurement is performed (Spekkens, 2005).”
A Combinatorial Approach to Nonlocality and Contextuality (2012, background): “The assumption of measurement noncontextuality [90] means that any reasonable theory should represent such a shared outcome as a function from states to probabilities which does not depend on the particular measurement in which the outcome occurs.”
Is the Quantum State Real? An Extended Review of -ontology Theorems (2014, methodology): “Gaussian functions are in fact positive so in this case W(x, p) can be regarded as a probability distribution and unsurprisingly these are the epistemic states in Spekkens’ continuous variable theory, with the ontic states being the phase space points (x, p).”
Quantum-Bayesian Coherence (2009, methodology): “We add this alternative formulation so as to place the discussion within the context of various other analyses of the idea of ‘contextuality’ [122, 123, 124, 125, 126].”