Violation of Bell inequalities in $2\times3$ dimensional systems

TL;DR

This paper analyzes the violation of Bell inequalities in a qubit-qutrit system, deriving conditions for violation and highlighting the role of local parameters.

Contribution

It provides necessary and sufficient conditions for Bell-CH inequality violation in 2x3 systems and emphasizes the significance of local parameters.

Findings

Derived conditions for Bell-CH violation in 2x3 systems

Identified families of states violating the inequality without correlation alone

Highlighted the importance of local parameters in Bell inequality violations

Abstract

We consider the Clauser-Horn (CH) inequality for a qubit-qutrit system. We derive the necessary and sufficient conditions for the violation of the inequality as well as some sufficient conditions. Remarkably, we demonstrate the importance of local parameters in violation of the inequality. In other words, there are some families of mixed states violating the inequality for which the correlation part alone is useless in the Bell-CH test.