  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.

Quantum Physics