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The aim is to establish the Tsirelson bound for the CHSH inequality, demonstrating its connection to root system A1 and octagonal symmetry.

August 2, 2026Open Access

Tsirelson Bound for CHSH Inequality: 2√2 from Root System A1 and Octagonal Symmetry — E8 Intelligence Research

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The aim is to establish the Tsirelson bound for the CHSH inequality, demonstrating its connection to root system A1 and octagonal symmetry.
Calculated the Tsirelson bound and its optimal violation through specific quantum observables.
Explored the mathematical framework connecting the CHSH inequality with geometric properties of SU(2) and octagonal symmetry.
Analyzed the relationship between optimal measurement angles and their implications for quantum nonlocality.
The Tsirelson bound for the CHSH inequality is established as 2√2 ≈ 2.828, indicating a fundamental limit on quantum correlations.
Optimal violation is realized with specific observables A and B, showing the influence of geometric symmetry on measurement directions.
The derived 45° angle between bases reflects octagonal symmetry, indicating a deep geometric relationship in quantum mechanics.

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This theoretical exploration uncovers quantum limits on correlation in a mathematical framework, suggesting implications for quantum nonlocality.

Andrew Stewart Caldin (2026) studied this question.

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This theoretical exploration uncovers quantum limits on correlation in a mathematical framework, suggesting implications for quantum nonlocality.