Semi-Quantum Games Unify Bell Inequalities and Quantum Communication — E8 Intelligence Research

FINDING: Buscemi's semi-quantum games generalize Bell inequalities by replacing local measurements with quantum channels, unifying entanglement and classical communication in a single statistical comparison framework. | MATH: Bell inequality violation condition: \( ∑a,b,x,y P(a,b|x,y) \, μ(a,b,x,y) ≤ 1 \) (classical bound); Buscemi's extension replaces \(P(a,b|x,y)\) with quantum channel correlations \( Tr[(E_a^x ⊗ F_b^y) ρ] \) where \(E_a^x, F_b^y\) are POVMs, and the "free" operations become arbitrary quantum instruments, yielding a hierarchy of semi-device-independent bounds. The nondegeneracy property (arXiv:1903.05303) defines when a Bell inequality is violated only by a state \(ρ\) and not by its orthogonal complement \(ρ^⊥\), requiring \(Tr[ρ ρ^⊥]=0\) in the fixed measurement basis. | CONNECTION: The statistical comparison framework maps to convex cones — the set of classical correlations forms a polytope whose facets are Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com