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 bases. Using this measure, we derive a “lower bound for the upper bound” in three and four real dimensions.
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© 2007 American Institute of Physics.
2007
American Institute of Physics
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