Entanglement Quantification via Bell Violation and Nondegeneracy — E8 Intelligence Research

Abstract

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 \(\rho\) of dimension \(d\) violates \(B\) (i.e., \(\langle B\rangle_\rho > \beta_{\text{local}}\)), then its orthogonal complement \(\rho^\perp\) (with \(\text{Tr}(\rho\rho^\perp)=0\)) cannot also violate \(B\) under the same measurements. This yields a dimension-witness bound: \(\text{Ent}(\rho) \geq f(\langle B\rangle_\rho, d)\) 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