An infinite family of Kochen-Specker sets in four-dimensional real spaces

Contextuality is a feature differentiating between classical and quantum physics. It is anticipated that it may become an important resource for quantum computing and quantum information processing. Contextuality was asserted by the Kochen-Specker (KS) theorem. We study parity proofs of the KS theorem. Although many parity proofs exist, only finitely many of them have been discovered in any real or complex space of fixed dimension. We study a special family of chordal ring graphs. We construct orthonormal representations of their line graphs in four-dimensional real spaces. Our construction takes advantage of the high degree of symmetry present in the special class of chordal rings that we use. In this way we find, for the first time, an infinite family of KS sets in a fixed dimension.