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Value-indefinite observables are almost everywhere

2013/09/30 by Alastair A. Abbott, Cristian S. Calude, Karl Svozil · 2 citations
Arts and Humanities · Computer Science · Physics and Astronomy · #Philosophy and History of Science #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.89.032109

published as Phys. Rev. A 89, 032109 (2014) · 18 pages, 5 figures

arxiv created 2014/03/10 · openalex publication_date 2014/03/10 · arxiv updated 2014/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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