KS uncolorability in 3D occurs only with modulus-2 or phase cancellation in the coordinate generators, producing new graph types in the Heegner-7 ring and golden ratio field.
The contextual fraction as a measure of contextuality
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abstract
We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of contextuality across measurement scenarios; it bears a precise relationship to violations of Bell inequalities; its value, and a witnessing inequality, can be computed using linear programming; it is monotone with respect to the "free" operations of a resource theory for contextuality; and it measures quantifiable advantages in informatic tasks, such as games and a form of measurement based quantum computing.
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The Algebraic Landscape of Kochen-Specker Sets in Dimension Three
KS uncolorability in 3D occurs only with modulus-2 or phase cancellation in the coordinate generators, producing new graph types in the Heegner-7 ring and golden ratio field.