Quaternions, octonions, and Bell-type inequalities

2008/03/06 by E. Shchukin, W. Vogel · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.78.032104

4 pages, no figures

arxiv created 2008/03/06 · openalex publication_date 2008/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Multipartite Bell-type inequalities are derived for general systems. They involve up to eight observables with arbitrary spectra on each site. These inequalities are closely related to the algebras of quaternions and octonions.

Citations

• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Quantum Nonlocality and Partial Transposition for Continuous-Variable Systems
• Bell Inequalities for Continuous-Variable Correlations
• On the Einstein Podolsky Rosen paradox
• Can Quantum-Mechanical Description of Physical Reality be Considered Complete?

Cited by

• Continuous-variable supraquantum nonlocality

Related

• Quaternion Analysis
• Bell's Inequalities and Algebraic Structure
• The structure of Bell inequalities
• Violation of Bell inequalities for multipartite systems
• An approach using geometric diagrams to generic Bell inequalities with multiple observables