Quaternions, octonions and Bell-type inequalities
E. Shchukin, W. Vogel
TL;DR
This paper derives multipartite Bell-type inequalities involving up to eight observables, linking their structure to quaternion and octonion algebras, advancing the understanding of quantum correlations.
Contribution
It introduces new Bell-type inequalities based on quaternion and octonion algebra structures for complex multipartite systems.
Findings
Derived inequalities for systems with up to eight observables
Connected algebraic structures to quantum nonlocality
Provides tools for testing quantum correlations
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.
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Taxonomy
TopicsQuantum Mechanics and Applications · Origins and Evolution of Life · Algebraic and Geometric Analysis