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I'm trying to understand what contextuality means in quantum mechanics (-> Kochen-Specker theorem). Can someone describe '(non-)contextuality' in a mathematical way? Wikipedia says something like 'the outcome of a measurement depends on its context (how the measurement is made)', which is not very satisfying.

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This tacit assumption that a hidden-variables theory has to assign to an observable $A$ the same value whether $A$ is measured as part of the mutually commuting set $A, B, C, \dots$ or a second mutually commuting set $A, L, M, \dots$ even when some of the $L, M, \dots$ fail to commute with some of the $B, C, \dots$, is called “non-contextuality” by the philosophers.

Source.

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