Is there contextuality for a single qubit?

Details Is there contextuality for a single qubit? Is there contextuality for a single qubit?

2007-05-01

arxiv.org/abs/0705.0181v2

Phys. Rev. Lett. 100, 160401 (2008)

Physics

Quantum Physics

4 pages, 1 figure, comments welcome

Scientific paper

10.1103/PhysRevLett.100.160401

It was presented by Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)], that the Kochen-Specker theorem applies to two dimensions if one uses Positive Operator-Valued Measures. We show that contextuality in their models is not of the Kochen-Specker type. It is rather the result of not keeping track of the whole system on which the measurement is performed. This is connected to the fact that there is no one-to-one correspondence between POVM elements and projectors on the extended Hilbert space and the same POVM element has to originate from two different projectors when used in Cabello's and Nakamura's models. Moreover, we propose a hidden-variable formulation of the above models.

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