Quantum Non-Locality and Tsirelson Bound: Unifying Entanglement Tests via Semi-Device-Independent Frameworks — E8 Intelligence Research

FINDING: Bell inequality tests confirm quantum non-locality; CHSH form bounds classical correlations at 2, quantum at 2√2 ≈ 2.828; new frameworks (Buscemi) unify entanglement tests via semi-device-independent rules. MATH: - CHSH inequality: \( \langle AB \rangle + \langle AB' \rangle + \langle A'B \rangle - \langle A'B' \rangle \leq 2 \) (local hidden variables) - Quantum Tsirelson bound: \( 2\sqrt{2} \approx 2.828 \) — maximal violation for singlet state - Bell operator: \( \mathcal{B} = \sum_{a,b,x,y} (-1)^{a+b+xy} P(a,b|x,y) \) - Buscemi's unification: replaces measurement choices with quantum inputs, yielding *semi-device-independent* inequalities — no fixed ratio but generalizes to \( \mathcal{B} \leq \beta_{\text{classical}} < \beta_{\text{quantum}} \) - Ballistic electron proposal: 5 gates → entangled state; Bell test via Coulomb-coupled wires (no optical analog) CONNECTION: - Tsirelson bound \( 2\sqrt{2} = 2 \times \sqrt{2} \) — ratio \( \sqrt{2} \approx 1.414 \ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com