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arXiv:quant-ph/9709047 · Physical Review Letters

Proposed Experimental Tests of the Bell-Kochen-Specker Theorem

Adán Cabello, Guillermo García Alcaine

Published Mar 2, 1998• 116 citations
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Abstract

For a two-particle two-state system, sets of compatible propositions exist for which quantum mechanics and noncontextual hidden-variable theories make conflicting predictions for every individual system whatever its quantum state. This permits a simple all-or-nothing state-independent experimental verification of the Bell-Kochen-Specker theorem.

DOI
10.1103/physrevlett.80.1797

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For a two-particle two-state system, sets of compatible propositions exist for which quantum mechanics and noncontextual hidden-variable theories make conflicting predictions for every individual system whatever its quantum state. This permits a simple all-or-nothing state-independent experimental verification of the Bell-Kochen-Specker theorem.
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We propose a feasible Kochen–Specker experiment with single photons, whose goal is to submit noncontextual hidden-variable theories to nonstatistical, all-or-nothing tests. Our proposal improves some recently performed tests in two respects. First, the present proposal is state-independent, thereby realizing a scheme designed by Cabello and García-Alcaine that was only partially realized in recent experiments. Second, our proposal can deal with non-ideal detectors without invoking the fair sampling assumption.
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of locality, Bell's theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS). Noncontextuality is independent of nonlocality, and the contextuality manifests itself even in a single object. Here we report an experimental verification of quantum contextuality by a single spin-1 electron system at room temperature. Such a three-level system is indivisible and then we close the compatibility loophole which exists in the experiments performed on bipartite systems. Our results confirm the quantum contextuality to be the intrinsic property of single particles.