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Exact projector-rank thresholds for state-independent contextuality

Primarily AI-generated textHuman understanding: some partsquant-ph — Quantum Physicsmath.CO — Combinatorics

Contributed by Sunay Venkat ↗

Version 1 / Nov 12, 2026 / CC BY 4.0

Abstract

For every integer r ≥ 1 we construct a finite exclusivity graph Fr with the following two properties. First, Fr has a projective representation by pairwise distinct projectors of rank r that exhibits state-independent contextuality. Second, no projective representation of Fr by projectors of any common rank s < r, in any finite dimension, exhibits state-independent contextuality; in every such representation the maximally mixed state is noncontextual. This establishes, for every r, the “rank efficient” scenarios sought by Hohn, Xu and Kleinmann, for which only numerical evidence at r = 2, 3 was available. The graph is the disjunctive product of an odd cycle C2r+1 with the orthogonality structure of a rank-one contextuality set whose fractional chromatic number exceeds its dimension by an arbitrarily small amount. Such sets are obtained from the infinite family of Kochen–Specker parity proofs in R^4 of Elford and Lisonek, together with a coning construction that raises the dimension by one.

Provenance statement

The proof was written by Anthropic's Fable 5.2, and verified by myself and OpenAI's GPT-6 Astra. I understand and verify the foundation of this proof, as it pulls from Westberg's paper; all additional work was verified by Astra.

References

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Show all 13 referencesShow fewer references
  1. G. Westberg, Unbounded projector-rank thresholds for state-independent contextuality , Zenodo, version 1.0.0, deposited 9 November 2026 (manuscript dated 6 November 2026), https://doi.org/10.5281/zenodo.24074025.DOI
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Version history

  1. v1 · 6 pagesSubmitted by Sunay VenkatInitial depositCurrentNov 11, 2026