Kochen and Specker's view on functional relations conflicts with the collapse postulate

Abstract: A key ingredient of the Kochen-Specker theorem is the so-called functional composition principle, which asserts that hidden states must ascribe values to observables in a way that is consistent with all functional relations between them. This principle is motivated by the assumption that, like functions of observables in classical mechanics, a function $g(A)$ of an observable A in quantum theory is simply a logically possible observable derived from $A$, and that measuring $g(A)$ consists in measuring $A$ and post-processing the resulting value via $g$. In this paper we show that, under suitable conditions, this reasonable assumption is in conflict with the collapse postulate. We then discuss possible solutions to this conflict, and we argue that the most justifiable and less radical one consists in adapting the collapse postulate by taking measurement contexts into account. This dependence on contexts arises for precisely the same reason why noncontextual hidden-variable models are ruled out by the Kochen-Specker theorem, namely that an observable A can typically be written as a function $A=g(B)=h(C)$ of noncommuting observables $B,C$.