  We give a new proof of the fact that the parallel repetition of the
(3-player) GHZ game reduces the value of the game to zero polynomially quickly.
That is, we show that the value of the $n$-fold GHZ game is at most
$n^{-\Omega(1)}$. This was first established by Holmgren and Raz [HR20]. We
present a new proof of this theorem that we believe to be simpler and more
direct. Unlike most previous works on parallel repetition, our proof makes no
use of information theory, and relies on the use of Fourier analysis.
  The GHZ game [GHZ89] has played a foundational role in the understanding of
quantum information theory, due in part to the fact that quantum strategies can
win the GHZ game with probability 1. It is possible that improved parallel
repetition bounds may find applications in this setting.
  Recently, Dinur, Harsha, Venkat, and Yuen [DHVY17] highlighted the GHZ game
as a simple three-player game, which is in some sense maximally far from the
class of multi-player games whose behavior under parallel repetition is well
understood. Dinur et al. conjectured that parallel repetition decreases the
value of the GHZ game exponentially quickly, and speculated that progress on
proving this would shed light on parallel repetition for general multi-player
(multi-prover) games.
