Construction of Kochen-Specker Sets from Mutually Unbiased Bases

• URL: http://arxiv.org/abs/2509.08636v1
• Date: Wed, 10 Sep 2025 14:32:24 GMT
• Title: Construction of Kochen-Specker Sets from Mutually Unbiased Bases
• Abstract summary: We show that contexts are crucial carriers of Kochen-Specker type logic and are indispensable for a rigorous assessment of quantum contextuality.<n>We generate a complete inventory of 165 rays and 130 bases from mutually unbiased bases.<n>Our findings establish that contexts are the crucial carriers of Kochen-Specker type logic and are indispensable for a rigorous assessment of quantum contextuality.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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