# Bell inequalities for $S_4$ group: classical and quantum bounds for two orbits case

## TL;DR

This paper explores Bell inequalities related to the $S_4$ group, analyzing classical and quantum bounds for systems with two orbits, and finds that violations are infrequent and mild.

## Contribution

It introduces specific classical and quantum bounds for Bell inequalities associated with the $S_4$ group and two orbits, expanding understanding of their violation patterns.

## Key findings

- Violations of Bell inequalities are rare
- Violations tend to be gentle or mild
- Classical and quantum bounds are explicitly characterized

## Abstract

Within Guney-Hillery approach a number of examples of classical and quantum bounds on sum of probabilities resulting from two orbits of $S_4$ is considered. It is shown that the violation of Bell's inequalities is rather rare and gentle.