Quantum Strategies for Simple 2-player XOR Games.

The non local game scenario is a powerful framework to study the limitations of classical and quantum correlations, in the interesting context where one does not look at the correlations themselves, but rather, to the upper bounds on the wining probabilities those correlations offer in cooperation games where communication between players is prohibited. Building upon the results presented in the well known paper of R.Cleve et al., this work shows a straightforward construction to compute the Tsirelson bounds for simple 2-player XOR games. The construction is applied explicitly to some examples, including \v{C}.Brukner et al. "Entanglement Assisted Orientation in Space" (EAOS) game, proving for the first time that their proposed quantum strategy is in fact the optimal, as it reaches the Tsirelson bound.