Exceptional and Non-crystallographic Root Systems and the Kochen-Specker Theorem

Understand

The Kochen-Specker theorem states that a 3-dimensional complex Euclidean space admits a finite configuration of projective lines such that the corresponding quantum observables (the orthogonal projectors) cannot be assigned with 0 and 1 values in a classically consistent way.

• This paper shows that the irreducible root systems of exceptional and of non-crystallographic types are useful in constructing such configurations in other dimensions.
• The cases $E_6$ and $E_7$ lead to new examples, while $F_4$, $E_8$, and $H_4$, yield a new interpretation of the known ones.
• The described configurations have an additional property: they are saturated, i.e.