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

Abstract

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: \( \sum_{a,b,x,y} P(a,b|x,y) \, \mu(a,b,x,y) \leq 1 \) (classical bound); Buscemi's extension replaces \(P(a,b|x,y)\) with quantum channel correlations \( \mathrm{Tr}[(E_a^x \otimes F_b^y) \rho] \) 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 \(\rho\) and not by its orthogonal complement \(\rho^\perp\), requiring \(\mathrm{Tr}[\rho \rho^\perp]=0\) 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