2025/09/10 by Mirko Navara, Karl Svozil, Navara, Mirko +1 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2509.08636
openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a systematic, constructive analysis of Kochen-Specker contextuality, emphasizing the foundational importance of complete orthogonal bases (contexts). First, in three dimensions, we generate a complete inventory of 165 rays and 130 bases from mutually unbiased bases. This unified framework reveals that several known constructions are equivalent manifestations of a minimal 69-ray, 50-context Kochen--Specker nucleus and uncovers a striking 40-4-4 generative asymmetry among the mutual unbiased bases, which we explain via the algebraic exclusivity of the Fourier basis. Second; in higher dimensions (D=4, 5), we develop explicit "forcing gadgets" that use orthogonality constraints to compel a central vector into a state of maximal unbiasedness. We demonstrate that our 20-vector gadget in D=4 and the 18-vector Cabello set are informationally equivalent subsets of the Peres--Mermin eigensystem, yet differ in their contextuality due to the choice of basis completions. Our findings establish that contexts, not merely intertwining vectors, are the crucial carriers of Kochen-Specker type logic and are indispensable for a rigorous assessment of quantum contextuality.