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arXiv · 1010.3733

Quantum contextuality for rational vectors

Adan Cabello·Jan-Åke Larsson
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Abstract

The Kochen-Specker theorem states that noncontextual hidden variable models are inconsistent with the quantum predictions for every yes-no question on a qutrit, corresponding to every projector in three dimensions. It has been suggested [D. A. Meyer, Phys. Rev. Lett. 83, 3751 (1999)] that the inconsistency would disappear when we are restricted to projectors on unit vectors with rational components; that noncontextual hidden variables could reproduce the quantum predictions for rational vectors. Here we show that a qutrit state with rational components violates an inequality valid for noncontextual hidden-variable models [A. A. Klyachko et al., Phys. Rev. Lett. 101, 020403 (2008)] using rational projectors. This shows that the inconsistency remains even when using only rational vectors.

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Adan Cabello, Jan-Åke Larsson. 2010-10-18. Quantum contextuality for rational vectors. https://doi.org/10.1016/j.physleta.2010.10.061

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