A closed-form necessary and sufficient condition for any two-qubit state to show hidden nonlocality w.r.t the Bell-CHSH inequality

TL;DR

This paper derives a precise mathematical condition for two-qubit states to exhibit hidden nonlocality under Bell-CHSH tests, and uses it to quantify how common such states are.

Contribution

It provides a closed-form necessary and sufficient criterion for hidden nonlocality in two-qubit states with respect to Bell-CHSH inequality, enabling numerical volume estimation.

Findings

Derived a closed-form condition for hidden nonlocality

Quantified the volume of states showing hidden Bell-CHSH nonlocality

Applied the condition to states with maximally mixed one-sided reduction

Abstract

In this note, we discuss a closed-form necessary and sufficient condition for any two-qubit state to show hidden nonlocality w.r.t the Bell-CHSH inequality. This is then used to numerically compute the relative volume of states showing hidden Bell-CHSH non-locality , among all two-qubit states with one-sided reduction maximally mixed.