Incomplete Kochen-Specker coloring

Journal Article · Sat Sep 15 00:00:00 EDT 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2779764· OSTI ID:21013632

Granstroem, Helena ^[1]

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1. Department of Mathematics, Stockholm University, SE-10691 Stockholm (Sweden) and Department of Physics, Stockholm University, SE-10691 Stockholm (Sweden)

A particular incomplete Kochen-Specker coloring, suggested by Appleby [Stud. Hist. Philos. Mod. Phys. 36, 1 (2005)] in dimension three, is generalized to arbitrary dimension. We investigate its effectivity as a function of dimension, using two different measures. A limit is derived for the fraction of the sphere that can be colored using the generalized Appleby construction as the number of dimensions approaches infinity. The second, and physically more relevant measure of effectivity, is to look at the fraction of properly colored ON bases. Using this measure, we derive a ''lower bound for the upper bound'' in three and four real dimensions.

• OSTI ID: 21013632
• Journal Information: Journal of Mathematical Physics, Vol. 48, Issue 9; Other Information: DOI: 10.1063/1.2779764; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HILBERT SPACE
QUANTUM MECHANICS
SPHERES