Bell inequality for qubits based on the Cauchy-Schwarz inequality

TL;DR

This paper introduces a systematic method for deriving Bell inequalities for qubits using the Cauchy-Schwarz inequality, classifies known inequalities via their roots, and presents new tight inequalities for three and four qubits.

Contribution

It provides a novel, systematic approach to derive and classify Bell inequalities for qubits, including the discovery of new tight inequalities.

Findings

Developed a method based on Cauchy-Schwarz inequality for Bell inequalities.

Classified Bell inequalities using the concept of roots of Bell functions.

Presented three new tight Bell inequalities for three and four qubits.

Abstract

We develop a systematic approach to establish Bell inequalities for qubits based on the Cauchy-Schwarz inequality. We also use the concept of distinct "roots" of Bell function to classify some well-known Bell inequalities for qubits. As applications of the approach, we present three new and tight Bell inequalities for four and three qubits, respectively.