contextuality

Contextuality is a feature of quantum mechanics and quantum information theory describing how the outcome of a measurement can depend on the set of other measurements performed alongside it, i.e., the measurement context. In a noncontextual hidden-variable model, each observable has a preassigned value that is independent of which compatible measurements are measured together; the outcome merely reveals that value. Quantum theory defies this assumption in systems of dimension three or higher, meaning that no such noncontextual assignment can reproduce all quantum predictions.

The Kochen-Specker theorem formalizes this limitation by showing that it is impossible to assign consistent, context-independent values to all quantum observables that obey their algebraic relations. Contextuality can be demonstrated through specific configurations of measurements (for example, certain sets of commuting observables arranged in parity or cycle structures) where the predicted statistics cannot be explained by any noncontextual model. Contextuality can be state-dependent (only certain quantum states reveal contextuality) or state-independent (contextuality manifests in all states).

Experiments testing contextuality typically use sequences of compatible measurements on systems such as photons or ions. While early tests faced loopholes related to measurement incompatibility and finite precision, recent work has strengthened evidence for quantum contextuality by closing or mitigating several of these issues.

Beyond foundational interest, contextuality is recognized as a resource for quantum information processing and quantum computation. The generalized notion of contextuality, including preparation, transformation, and measurement contextuality, has been formalized by Spekkens and connected to tasks where quantum advantage arises.