# Note on G\"uney-Hillery approach to Bell inequalities

## TL;DR

This paper examines the group-theoretical method for deriving Bell inequalities, focusing on the conditions under which these inequalities are violated or satisfied, especially in the context of real representations and maximally entangled states.

## Contribution

It clarifies the construction of Bell inequalities via group orbits and identifies when violations occur, particularly highlighting the role of real representations and entanglement.

## Key findings

- Bell inequalities are not violated for real representations with trivial subrepresentations in the single orbit case.
- The group-theoretical approach provides a systematic way to derive Bell inequalities.
- Maximally entangled states do not violate Bell inequalities under certain group representation conditions.

## Abstract

We analyze certain aspects of group theoretical approach to Bell inequalities proposed by G\"uney and Hillery. The general procedure for constructing the relevant group orbits is described. Using Hall theorem we determine the form of Bell inequality in the single orbit case. It is shown that in this case the Bell inequality is not violated for maximally entangled state generating trivial subrepresentation if the representation under consideration is real.