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arXiv · 1309.7188

Value-indefinite observables are almost everywhere

Alastair A. Abbott·Cristian S. Calude·Karl Svozil
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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. It was recently shown [Phys. Rev. A 86, 062109 (2012)] that this breakdown does not occur everywhere; here we show that it 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 occur with certainty, almost (i.e. with Lebesgue measure one) all remaining observables are indeterminate.

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Alastair A. Abbott, Cristian S. Calude, Karl Svozil. 2014-03-10. Value-indefinite observables are almost everywhere. https://doi.org/10.1103/physreva.89.032109

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