quantum algorithms:
In quantum physics and in particular in the context of hidden variable theories (cf. interpretation of quantum mechanics) the term (quantum) contextuality refers to the (assumed) dependence of the value of quantum observables not just on (hypothetical) hidden variables but also on a specified “context” of other compatible (commuting) observables.
The notion originates in the discussion of the Bell-Kochen-Specker theorem which rules out the assumption that quantum observables all at once jointly dependent (only) on “hidden variables”. However, for any chosen commutative subalgebra of observables the assumption is valid (cf. Bohr topos), whence one may consider the idea that observables are defined by hidden variables and the specification of such “contexts”, hence that quantum observables are “contextual”.
Textbook accoutn:
See also:
Sheaf-theoretic aspects:
Cohomological aspects:
and via (singular cohomology of) simplicial sets:
Cihan Okay, Sam Roberts, Stephen D. Bartlett, Robert Raussendorf, Topological proofs of contextuality in quantum mechanics, Quantum Information and Computation 17 (2017) 1135-1166 [arXiv:1701.01888, doi:10.26421/QIC17.13-14-5]
Cihan Okay, Aziz Kharoof, Selman Ipek, Simplicial quantum contextuality, Quantum 7 (2023) 1009 [arXiv:2204.06648, doi:10.22331/q-2023-05-22-1009]
Aziz Kharoof, Cihan Okay, Homotopical characterization of strongly contextual simplicial distributions on cone spaces [arXiv:2311.14111]
exposition:
Probabilistic aspects:
Last revised on November 27, 2023 at 10:28:44. See the history of this page for a list of all contributions to it.