The generalized Kochen-Specker theorem

Abstract

A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker and Bell theorems that shed some light on the relationship between these three theorems.

5 pages, 1 Table. A new third paragraph and an additional reference have been added

References in corpus (3)

• Hidden Variables and the Two Theorems of John Bell
• "All versus nothing" inseparability for two observers
• Kochen-Specker theorem for a single qubit using positive operator-valued measures

Cited by in corpus (7)

• Kochen-Specker Vectors
• The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory
• Experimental generalized contextuality with single-photon qubits
• Implementation of group-covariant POVMs by orthogonal measurements
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Is there contextuality for a single qubit?
• On the connection between the theorems of Gleason and of Kochen and Specker