Analysis of Boolean Functions Related to Binary Input Binary Output Two-party Nonlocal Games

TL;DR

This paper exhaustively analyzes Boolean functions for four variables to identify two-party nonlocal games with higher quantum success probabilities than classical ones, highlighting the CHSH game as most efficient for quantum-classical separation.

Contribution

It provides a comprehensive study of all four-variable Boolean functions in nonlocal games, discovering new games with improved quantum success rates over classical strategies.

Findings

Some nonlocal games outperform CHSH in quantum success probability

CHSH game remains the most efficient for quantum-classical separation

Identifies specific Boolean functions that enhance quantum advantage

Abstract

The famous CHSH game can be interpreted with Boolean functions while understanding the success probability in the classical scenario. In this paper, we have exhaustively studied all the Boolean functions on four variables to express binary input binary output two-party nonlocal games and explore their performance in both classical and quantum scenarios. Our analysis finds out some other games (other than the CHSH game) which offer a higher success probability in the quantum scenario as compared to the classical one. Naturally, our study also notes that the CHSH game (and the games corresponding to the similar partition) is the most efficient in terms of separation between quantum and classical techniques.