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

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 $O(q^{-1})$.

11 pages, 3 figures

References in corpus (4)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Device-independent security of quantum cryptography against collective attacks
• Multi-setting Bell inequality for qudits
• Device-independent randomness extraction for arbitrarily weak min-entropy source

Cited by in corpus (1)

• Tight bound on the classical value of generalized Clauser-Horne-Shimony-Holt games