Quantum contextuality

Quantum contextuality is the impossibility of reproducing quantum measurement statistics with predetermined outcomes that are independent of which compatible measurements are performed together.

Kochen–Specker theorem: A theorem showing that quantum observables cannot be assigned context-independent values while preserving functional relations among them. It establishes contextuality through the impossibility of a consistent value assignment.
John Bell: A physicist who proved that local hidden-variable theories satisfy inequalities violated by quantum predictions. Bell emphasized that the Kochen–Specker result concerns contextuality distinct from spatial nonlocality.
Contextuality inequality: An inequality obeyed by noncontextual models but violated by quantum measurement statistics. Violations provide experimentally testable witnesses of contextuality.
Bell theorem: A result showing that no theory satisfying Bell-locality and measurement independence can reproduce all quantum correlations. It rules out local explanations, whereas contextuality concerns dependence on compatible measurement arrangements.
Spekkens contextuality: An operational notion of contextuality that tests whether ontological models assign equivalent procedures equivalent representations. It extends contextuality beyond sharp measurements and traditional value-assignment theorems.
Peres–Mermin square: A compact arrangement of two-qubit observables whose commuting products yield a contradiction for noncontextual value assignments. This finite example exposes the contradiction with a small set of measurements.
Simon Kochen: A mathematician who co-authored the theorem ruling out noncontextual value assignments for quantum observables. His 1967 work with Ernst Specker gave contextuality its foundational theorem.
Quantum contextuality experiment: An experiment that tests contextuality by measuring compatible observables and comparing their statistics with noncontextual bounds. Laboratory tests turn the no-go result into observed statistical violations.
Bell inequality: A bound on correlations predicted by local hidden-variable theories that quantum experiments can violate. Its violations test locality assumptions rather than noncontextuality alone.
Preparation contextuality: Contextuality in which operationally equivalent state preparations cannot share the same hidden-variable representation. It asks whether contextuality can be witnessed through preparations rather than measurement outcomes.

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