Partial list of bipartite Bell inequalities with four binary settings

TL;DR

This paper presents a partial list of 26 tight bipartite Bell inequalities with four measurement settings, analyzing their quantum violations, noise resistance, and detection efficiency, revealing that many are less effective than CHSH.

Contribution

It provides a new partial catalog of Bell inequalities with detailed numerical analysis, expanding understanding of measurement settings in quantum nonlocality.

Findings

Most inequalities are outperformed by CHSH in quantum violation

Analysis of noise resistance and detection efficiency for each inequality

Partial list of tight Bell inequalities with four measurement settings

Abstract

We give a partial list of 26 tight Bell inequalities for the case where Alice and Bob choose among four two-outcome measurements. All tight Bell inequalities with less settings are reviewed as well. For each inequality we compute numerically the maximal quantum violation, the resistance to noise and the minimal detection efficiency required for closing the detection loophole. Surprisingly, most of these inequalities are outperformed by the CHSH inequality.