Bell - Kochen - Specker theorem for any finite dimension
- 7 March 1996
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 29 (5), 1025-1036
- https://doi.org/10.1088/0305-4470/29/5/016
Abstract
The Bell - Kochen - Specker theorem against non-contextual hidden variables can be proved by constructing a finite set of `totally non-colourable' directions, as Kochen and Specker did in a Hilbert space of dimension n = 3. We generalize Kochen and Specker's set to Hilbert spaces of any finite dimension , in a three-step process that shows the relationship between different kinds of proofs (`continuum', `probabilistic', `state-specific' and `state-independent') of the Bell - Kochen - Specker theorem. At the same time, this construction of a totally non-colourable set of directions in any dimension explicitly solves the question raised by Zimba and Penrose about the existence of such a set for n = 5.Keywords
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