TL;DR
This paper investigates the structure of Kochen-Specker sets in 3 and 4 dimensions, revealing a unique family of sets with shared orthogonality graphs and highlighting their distinctive parameter freedom compared to other sets.
Contribution
It identifies a three-parameter family of Kochen-Specker sets sharing the same orthogonality graph, contrasting with the parameter-free nature of other known sets.
Findings
Two sets form a 3-parameter family sharing the same orthogonality graph.
Most Kochen-Specker sets are fully determined by orthogonality, with no free parameters.
The identified family is unusual among known Kochen-Specker configurations.
Abstract
We look at generalisations of sets of vectors proving the Kochen-Specker theorem in 3 and 4 dimensions. It has been shown that two such sets, although unitarily inequivalent, are part of a larger 3-parameter family of vectors that share the same orthogonality graph. We find that these sets are unusual, in that the vectors in all other Kochen-Specker sets investigated here are fully determined by orthogonality conditions and thus admit no free parameters.
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