Abstract:
Kochen-Specker theorems assure the breakdown of certain types of non-contextual hidden variable theories
through the non-existence of global, holistic frame functions; alas they do not allow us to identify where
this breakdown occurs, nor the extent of it. Here we show that this breakdown is maximal in that it occurs
almost everywhere, and thus prove that quantum indeterminacy—often referred to as contextuality or value
indefiniteness—is a global property as is often assumed. In contrast to the Kochen-Specker theorem, we
only assume the weaker non-contextuality condition that any potential value assignments that may exist are
locally non-contextual. Under this assumption, we prove that once a single arbitrary observable is fixed to
be value definite, almost (i.e. with Lebesgue measure one) all remaining observables are indeterminate.