Abstract
For many protocols, quantum strategies have advantages compared with their classical counter-partners, and these advantages have attracted many interests and applications. One of the famous examples is the Clauser-Horne-Shimony-Holt (CHSH) game, which recasts Bell's theorem~\cite{2} into the framework of a game. In the CHSH game, two space-like separated players, Alice and Bob are each assigned a classical bit a and b respectively. Then they return bits x and y according to some pre-agreed strategies. They will win the game when x⊕ y= a· b. In the game, if the players use the classical strategies, the optimal success probability w(CHSH)=0.75.However, if they add some quantum resources, the success probability will increase and up to maximal value cos²(π/8), which is know as the Tsirelson's bound. Moreover, Popescu and Rohrlich noted that the perfect success probability 1 can also be achieved in a more general theory without violating the no-signaling assumption