2016/03/31 by Katarzyna Bolonek-Lasoń
Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Geometry #Homogeneous space #Mathematics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Relativity and Gravitational Theory #Tetrahedron #quant-ph
paper · pdf · doi:10.1103/physreva.94.022107
published as Phys. Rev. A 94, 022107 (2016) · 22 pages, 1 figure, final version accepted for publication in Physical Review A
arxiv created 2016/08/03 · openalex publication_date 2016/08/09 · arxiv updated 2016/08/17 · openalex created_date 2016/10/07 · openalex updated_date 2026/08/05
In two recent papers [Phys. Rev. A 90, 062121 (2014) and Phys. Rev. A, 91, 052110 (2015)] an interesting method of analyzing the violation of Bell inequalities has been proposed which is based on the theory of finite group representations. Here we apply this method to more complicated examples of S4 symmetry. We show how the Bell inequality can be related to the symmetries of regular tetrahedron. By choosing the orbits of three-dimensional representations of S4 determined by the geometry of tetrahedron we find that the Bell inequality under consideration is violated in quantum theory. The corresponding nonlocal game is analyzed.