On symmetric nonlocal games

Nonlocal games are used to display differences between the classical and quantum world. In this paper, we study symmetric XOR games, which form an important subset of nonlocal games. We give simple methods for calculating the classical and the quantum values for symmetric XOR games with one-bit input per player. We illustrate those methods with two examples. One example is an N-player game (due to Ardehali (1992) [3]) that provides the maximum quantum-over-classical advantage. The second example comes from generalization of CHSH game by letting the referee to choose arbitrary symmetric distribution of players' inputs.