Which Classicality? Incidence, Simplex, and Product-Rule Tests in Finite Quantum Logics
arXiv:2607.11234
The paper studies how finite quantum‑logical structures can be classified as classical or nonclassical using incidence, simplex‑embedding, and product‑rule tests, and calculates state‑depolarizing thresholds for selected fragments like GHZ contexts.
Abstract
Finite quantum-logical constructions can appear classical or nonclassical depending on which structure is retained. We distinguish incidence tests based on valuations, colorings, and partition representations; simplex-embedding tests for specified prepare-and-measure fragments; and operator-functional tests imposing spectral and product rules. We show that the collective GHZ joint measurement is a single Boolean context and becomes nonclassical only when a common assignment of local factors, together with product preservation, is required. For selected labelled ray fragments, we compute state-depolarizing thresholds for a restricted projector-cone factorization and for a specified vector-generated operational closure, separating exact primal--dual certificates from numerical estimates. These values are properties of the stated fragments and noise model, not invariants of the underlying hypergraphs or a universal ordering of contextuality.
22 pages, 3 tables