Quantum strategies for simple 2-player XOR games

TL;DR

This paper presents a method to compute Tsirelson bounds for simple 2-player XOR games and demonstrates its application by proving the optimality of a quantum strategy in the EAOS game.

Contribution

It introduces a straightforward construction for calculating Tsirelson bounds and applies it to confirm the optimality of a quantum strategy in a specific XOR game.

Findings

The construction simplifies Tsirelson bound calculations.

The quantum strategy in the EAOS game is proven optimal.

The method confirms quantum advantage in XOR games.

Abstract

The non-local game scenario provides a powerful framework to study the limitations of classical and quantum correlations, by studying the upper bounds of the winning probabilities those correlations offer in cooperation games where communication between players is prohibited. Building upon results presented in the seminal work of Cleve et al. [1], a straightforward construction to compute the Tsirelson bounds for simple 2-player XOR games is presented. The construction is applied explicitly to some examples, including the Entanglement Assisted Orientation in Space (EAOS) game of Brukner et al. [2], proving for the first time that their proposed quantum strategy is in fact the optimal, as it reaches the Tsirelson bound.