Vector space constructions of Kochen-Specker sets using Hadamard matrices
Phys. Rev. A 112, 032207 – Published 5 September, 2025
DOI: https://doi.org/10.1103/bdrr-q25l
Abstract
We analyze and generalize a construction method of Kochen-Specker (KS) sets given by Waegell and Aravind. In this method the bases that participate in a KS set are formed by modifying a seed basis using a vector space of shifts. We show that any real or generalized Hadamard matrix can be used as the seed basis, and that the space of shifts can be much smaller than originally proposed. Main benefits of these generalizations are a vastly extended set of available seed matrices, and significantly smaller KS sets produced. Analytical constructions of infinite families of Hadamard matrices combined with our generalized approach allow us to construct an infinite family of KS sets.
