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arXiv:quant-ph/0009074 · Physical Review Letters

Feasible “Kochen-Specker” Experiment with Single Particles

Christoph Simon, Marek Żukowski, Harald Weinfurter, Anton Zeilinger

Published Aug 28, 2000• 137 citations
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Abstract

We present a simple experimental scheme which can be used to demonstrate an all-or-nothing-type contradiction between noncontextual hidden variables and quantum mechanics. The scheme, which is inspired by recent ideas by Cabello and Garcia-Alcaine, shows that even for a single particle, path and spin information cannot be predetermined in a noncontextual way.

DOI
10.1103/physrevlett.85.1783

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We present a simple experimental scheme which can be used to demonstrate an all-or-nothing-type contradiction between noncontextual hidden variables and quantum mechanics. The scheme, which is inspired by recent ideas by Cabello and Garcia-Alcaine, shows that even for a single particle, path and spin information cannot be predetermined in a noncontextual way.
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.
Meyer [Phys. Rev. Lett. 83, 3751 (1999)] recently showed that the Kochen-Specker theorem, which demonstrates the impossibility of a deterministic hidden variable description of ideal spin measurements on a spin 1 particle, can be effectively nullified if only finite precision measurements are considered. We generalize this result: one can ascribe consistent outcomes to a dense subset of the set of projection valued measurements, or to a dense subset of the set of positive operator valued measurements, on any finite dimensional system. Hence no Kochen-Specker-like contradiction can rule out hidden variable theories indistinguishable from quantum theory by finite precision measurements in either class.