Quantum contextuality for rational vectors |
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Authors: | Adá n Cabello,Jan-Å ke Larsson |
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Affiliation: | a Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain b Institutionen för Systemteknik, Linköpings Universitet, SE-581 83 Linköping, Sweden |
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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 (1999) 3751] that the inconsistency would disappear when restricting 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 (2008) 020403] using rational projectors. This shows that the inconsistency remains even when using only rational vectors. |
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