Quantum contextuality

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.