Quantum contextuality for rational vectors

Details Quantum contextuality for rational vectors Quantum contextuality for rational vectors

2010-10-18

arxiv.org/abs/1010.3733v2

Phys. Lett. A 375 (2010) 99

Physics

Quantum Physics

REVTeX4-1, 1 page

Scientific paper

10.1016/j.physleta.2010.10.061

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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