Entanglement Quantification via Bell Violation and Nondegeneracy — E8 Intelligence Research

FINDING: Semi-device-independent entanglement quantification reduces to Bell-inequality violation bounds under fixed local measurements, with a "nondegeneracy" condition separating orthogonal quantum states by dimension. | MATH: Nondegeneracy property — for a Bell inequality \(B\) and fixed local measurements \(\{M_A^a, M_B^b\}\), if a state \(ρ\) of dimension \(d\) violates \(B\) (i.e., \( B_ρ > βlocal\)), then its orthogonal complement \(ρ^⊥\) (with \(Tr(ρρ^⊥)=0\)) cannot also violate \(B\) under the same measurements. This yields a dimension-witness bound: \(Ent(ρ) ≥ f( B_ρ, d)\) where \(f\) is monotonic in the Bell violation. | CONNECTION: The orthogonal-state separation mirrors root-system orthogonality (e.g., \(A_2\) root lattice angles at 60° and 120°), and the dimension constraint \(d\) acts like a lattice rank — violation strength maps to a radial coordinate in a convex set of quantum corre Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com