Is there contextuality for a single qubit?

Abstract

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.

4 pages, 1 figure, comments welcome

References in corpus (5)

• Hidden Variables and the Two Theorems of John Bell
• Contextuality for preparations, transformations, and unsharp measurements
• Quantum states and generalized observables: a simple proof of Gleason's theorem
• Kochen-Specker theorem for a single qubit using positive operator-valued measures
• The generalized Kochen-Specker theorem

Cited by in corpus (7)

• Quasi-probability representations of quantum theory with applications to quantum information science
• The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Demonstrating quantum contextuality of indistinguishable particles by a single family of noncontextuality inequalities
• Contextuality in bosonic bunching
• Quantum-mechanical machinery for rational decision-making in classical guessing game
• Quantum contextuality for a relativistic spin-1/2 particle