CHSH Inequalities as Unified Rules Linking Entanglement to Device-Independent Tests — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Bell/CHSH inequalities define the boundary between local-hidden-variable (classical) and quantum correlations; recent work (Buscemi) recasts them as a unified family of "rules" linking entanglement to device-independent tests. | MATH: CHSH form S = E(a,b) − E(a,b′) + E(a′,b) + E(a′,b′) ≤ 2 (LHV bound); quantum (Tsirelson) bound S_max = 2√2 ≈ 2.828. Quantum correlation set is strictly larger than the classical polytope but strictly smaller than the no-signaling polytope (PR-box value 4). | CONNECTION: 2√2 = 2·√2 is the Tsirelson constant; note √2 is the diagonal of the unit square and the ratio of the octahedron/cube dual pair. The CHSH polytope is a hypercube (8 vertices, 2⁴ sign choices) — a 4-dimensional measure polytope, one of the crystallographic/root-system family (B₄/C₄ symmetry). The classical bound 2 and quantum bound 2√2 differ by factor √2 ≈ 1.414, not a Fibonacci/φ ratio. No 0.618/1.618 structure appears in the inequality itself. | DEPTH: 7
Notes on the other item
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026chsh,
title = {{CHSH Inequalities as Unified Rules Linking Entanglement to Device-Independent Tests — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658616},
url = {https://zenodo.org/records/23658616},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - CHSH Inequalities as Unified Rules Linking Entanglement to Device-Independent Tests — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658616
UR - https://zenodo.org/records/23658616
AB - FINDING: Bell/CHSH inequalities define the boundary between local-hidden-variable (classical) and quantum correlations; recent work (Buscemi) recasts them as a unified family of "rules" linking entanglement to device-independent tests. | MATH: CHSH form S = E(a,b) − E(a,b′) + E(a′,b) + E(a′,b′) ≤ 2 (LHV bound); quantum (Tsirelson) bound S_max = 2√2 ≈ 2.828. Quantum correlation set is strictly larger than the classical polytope but strictly smaller than the no-signaling polytope (PR-box value 4). | CONNECTION: 2√2 = 2·√2 is the Tsirelson constant; note √2 is the diagonal of the unit square and the ratio of the octahedron/cube dual pair. The CHSH polytope is a hypercube (8 vertices, 2⁴ sign choices) — a 4-dimensional measure polytope, one of the crystallographic/root-system family (B₄/C₄ symmetry). The classical bound 2 and quantum bound 2√2 differ by factor √2 ≈ 1.414, not a Fibonacci/φ ratio. No 0.618/1.618 structure appears in the inequality itself. | DEPTH: 7 Notes on the other item Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -