In this talk, we consider a variant of entangled non-local games where the players are allowed to share infinitely many copies of noisy EPR states. We provide an upper bound on the copies of noisy EPR states for the players to approximate the values of games to an arbitrary precision if the games are binary. The arguments are built on the recent framework about the decidability of the non-interactive simulation of joint distributions with significant extension. A series new techniques on the Fourier analysis on random operator spaces are introduced including a quantum invariance principle and a hypercontractive inequality for random operators. These novel tools are interesting on their own right and may have further applications in quantum information theory and quantum complexity theory.