Kochen–Specker theorem

A no-go theorem showing that quantum observables cannot all have predetermined values independent of the compatible measurements performed alongside them.

Noncontextual hidden-variable theory: A theory in which measurement outcomes are predetermined and independent of which compatible measurements accompany each observable. This is the assumption the theorem shows cannot reproduce quantum predictions for all observables.
Quantum observable: A physical quantity represented by a self-adjoint operator in quantum theory. The theorem concerns whether every such quantity can carry a predetermined measurement value.
John Stewart Bell: A physicist whose work established constraints on hidden-variable theories and clarified quantum nonlocality. Bell analyzed the Kochen–Specker result and its relation to hidden-variable explanations.
Bell's theorem: A theorem showing that no theory satisfying Bell-locality can reproduce all quantum correlations. Unlike Bell's result, this theorem rules out noncontextual value assignments without assuming spatial separation.
Contextuality: Dependence of a measurement outcome on the other compatible measurements performed in the same context. The theorem establishes that quantum theory requires this dependence for predetermined-value accounts.
Commuting operators: Operators whose products are unchanged when their order is exchanged. Commuting observables can be measured jointly and form the contexts constrained by the theorem.
Simon Kochen: A mathematician who co-authored the 1967 theorem on value assignments in quantum mechanics. His work with Ernst Specker supplied the theorem's original finite-dimensional argument.
EPR paradox: A thought experiment arguing that quantum mechanics leaves physical reality incompletely described. The theorem addresses the hidden-variable program motivated by this challenge to quantum completeness.
Orthogonality graph: A graph whose vertices represent quantum states and whose edges connect orthogonal states. Graph constraints encode the exclusivity relations used in many proofs of the theorem.
Quantum measurement: A physical interaction that produces an outcome associated with an observable in quantum theory. The theorem compares measurement outcomes across different compatible measurement arrangements.

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