"Contextuality" redirects here. For the principle of contextuality in Linguistics, see context (linguistics).
Quantum contextuality is a feature of the phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as revealing pre-existing values. Any attempt to do so in a realistic hidden-variable theory leads to values that are dependent upon the choice of the other (compatible) observables which are simultaneously measured (the measurement context). More formally, the measurement result (assumed pre-existing) of a quantum observable is dependent upon which other commuting observables are within the same measurement set.
Contextuality was first demonstrated to be a feature of quantum phenomenology by the Bell–Kochen–Specker theorem.[1][2] The study of contextuality has developed into a major topic of interest in quantum foundations as the phenomenon crystallises certain non-classical and counter-intuitive aspects of quantum theory. A number of powerful mathematical frameworks have been developed to study and better understand contextuality, from the perspective of sheaf theory,[3] graph theory,[4] hypergraphs,[5] algebraic topology,[6] and probabilistic couplings.[7]
Nonlocality, in the sense of Bell's theorem, may be viewed as a special case of the more general phenomenon of contextuality, in which measurement contexts contain measurements that are distributed over spacelike separated regions. This follows from Fine's theorem.[8][3]
Quantum contextuality has been identified as a source of quantum computational speedups and quantum advantage in quantum computing.[9][10][11][12] Contemporary research has increasingly focused on exploring its utility as a computational resource.
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^Cite error: The named reference :2 was invoked but never defined (see the help page).
^ abAbramsky, Samson; Brandenburger, Adam (2011-11-28). "The Sheaf-Theoretic Structure Of Non-Locality and Contextuality". New Journal of Physics. 13 (11): 113036. arXiv:1102.0264. Bibcode:2011NJPh...13k3036A. doi:10.1088/1367-2630/13/11/113036. ISSN 1367-2630. S2CID 17435105.
^Acín, Antonio; Fritz, Tobias; Leverrier, Anthony; Sainz, Ana Belén (2015-03-01). "A Combinatorial Approach to Nonlocality and Contextuality". Communications in Mathematical Physics. 334 (2): 533–628. arXiv:1212.4084. Bibcode:2015CMaPh.334..533A. doi:10.1007/s00220-014-2260-1. ISSN 1432-0916. S2CID 119292509.
^Abramsky, Samson; Mansfield, Shane; Barbosa, Rui Soares (2012-10-01). "The Cohomology of Non-Locality and Contextuality". Electronic Proceedings in Theoretical Computer Science. 95: 1–14. arXiv:1111.3620. doi:10.4204/EPTCS.95.1. ISSN 2075-2180. S2CID 9046880.
^Dzhafarov, Ehtibar N.; Kujala, Janne V. (2016-09-07). "Probabilistic foundations of contextuality". Fortschritte der Physik. 65 (6–8): 1600040. arXiv:1604.08412. Bibcode:2017ForPh..6500040D. doi:10.1002/prop.201600040. ISSN 0015-8208. S2CID 56245502.
^Fine, Arthur (1982-02-01). "Hidden Variables, Joint Probability, and the Bell Inequalities". Physical Review Letters. 48 (5): 291–295. Bibcode:1982PhRvL..48..291F. doi:10.1103/PhysRevLett.48.291.
^Raussendorf, Robert (2013-08-19). "Contextuality in measurement-based quantum computation". Physical Review A. 88 (2): 022322. arXiv:0907.5449. Bibcode:2013PhRvA..88b2322R. doi:10.1103/PhysRevA.88.022322. ISSN 1050-2947. S2CID 118495073.
^Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph (June 2014). "Contextuality supplies the 'magic' for quantum computation". Nature. 510 (7505): 351–355. arXiv:1401.4174. Bibcode:2014Natur.510..351H. doi:10.1038/nature13460. ISSN 0028-0836. PMID 24919152. S2CID 4463585.
^Abramsky, Samson; Barbosa, Rui Soares; Mansfield, Shane (2017-08-04). "Contextual Fraction as a Measure of Contextuality". Physical Review Letters. 119 (5): 050504. arXiv:1705.07918. Bibcode:2017PhRvL.119e0504A. doi:10.1103/PhysRevLett.119.050504. ISSN 0031-9007. PMID 28949723. S2CID 206295638.
^Bermejo-Vega, Juan; Delfosse, Nicolas; Browne, Dan E.; Okay, Cihan; Raussendorf, Robert (2017-09-21). "Contextuality as a Resource for Models of Quantum Computation with Qubits". Physical Review Letters. 119 (12): 120505. arXiv:1610.08529. Bibcode:2017PhRvL.119l0505B. doi:10.1103/PhysRevLett.119.120505. ISSN 0031-9007. PMID 29341645. S2CID 34682991.
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