Breaking of Bell inequalities from $S_4$ symmetry: the three orbits case

TL;DR

This paper applies a group theoretical approach using the $S_4$ symmetry to derive and analyze Bell inequalities based on three orbits, exploring their violation and implications for nonlocal games.

Contribution

It extends previous group theoretical methods to the $S_4$ group, deriving new Bell inequalities and analyzing their breaking and nonlocal game applications.

Findings

Derived Bell inequalities from $S_4$ symmetry with three orbits

Analyzed the breaking of these inequalities

Explored implications for nonlocal games

Abstract

The recently proposed (Phys. Rev. A90 (2014), 062121 and Phys. Rev. A91 (2015), 052110) group theoretical approach to the problem of breaking the Bell inequalities is applied to $S_4$ group. The Bell inequalities based on the choice of three orbits in the representation space corresponding to standard representation of $S_4$ are derived and their breaking is described. The corresponding nonlocal games are analyzed.