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Journal of Modern Optics

A state-independent test of the Kochen–Specker theorem

F. De Zela

Published Feb 20, 2009• 2 citations
Publisher

Abstract

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.

DOI
10.1080/09500340802444295

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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.
A recent proposal to experimentally test quantum mechanics against noncontextual hidden-variable theories [Phys. Rev. Lett.80, 1797 (1998)] is shown to be related with the smallest proof of the Kochen–Specker theorem currently known [Phys. Lett.A212, 183 (1996)]. This proof contains eighteen yes-no questions about a four-dimensional physical system, combined in nine mutually incompatible tests. When these tests are considered as tests about a two-part two-state system, then quantum mechanics and noncontextual hidden variables make the same predictions for eight of them, but make different predictions for the ninth. Therefore, this ninth test would allow us to discriminate between quantum mechanics and noncontextual hidden-variable theories in a (gedanken) single run experiment.
The Kochen-Specker theorem demonstrates that it is not possible to reproduce the predictions of quantum theory in terms of a hidden variable model where the hidden variables assign a value to every projector deterministically and noncontextually. A noncontextual value assignment to a projector is one that does not depend on which other projectors-the context-are measured together with it. Using a generalization of the notion of noncontextuality that applies to both measurements and preparations, we propose a scheme for deriving inequalities that test whether a given set of experimental statistics is consistent with a noncontextual model. Unlike previous inequalities inspired by the Kochen-Specker theorem, we do not assume that the value assignments are deterministic and therefore in the face of a violation of our inequality, the possibility of salvaging noncontextuality by abandoning determinism is no longer an option. Our approach is operational in the sense that it does not presume quantum theory: a violation of our inequality implies the impossibility of a noncontextual model for any operational theory that can account for the experimental observations, including any successor to quantum theory.