An explicit classical strategy for winning a $\mathrm{CHSH}_{q}$ game

TL;DR

This paper presents a new explicit classical strategy for the generalized CHSH_q game with prime q, achieving a higher winning probability than previous strategies, advancing understanding of classical approaches in nonlocal games.

Contribution

The paper introduces a constructive classical strategy for CHSH_q games that surpasses previous winning probability bounds, specifically for prime q.

Findings

Achieves winning probability better than (1/22)q^(-2/3)

Improves upon previous strategies with winning probability of O(q^(-1))

Provides a concrete classical approach for prime q in CHSH_q games

Abstract

A $\mathrm{CHSH}_{q}$ game is a generalization of the standard two player $\mathrm{CHSH}$ game, having $q$ different input and output options. In contrast to the binary game, the best classical and quantum winning strategies are not known exactly. In this paper we provide a constructive classical strategy for winning a $\mathrm{CHSH}_{q}$ game, with $q$ being a prime. Our construction achieves a winning probability better than $\frac{1}{22}q^{-\frac{2}{3}}$, which is in contrast with the previously known constructive strategies achieving only the winning probability of $O(q^{-1})$.