A parallel repetition theorem for entangled projection games

Understand

We study the behavior of the entangled value of two-player one-round projection games under parallel repetition.

• We show that for any projection game $G$ of entangled value 1-eps < 1, the value of the $k$-fold repetition of G goes to zero as O((1-eps^c)^k), for some universal constant c\geq 1.
• Previously parallel repetition with an exponential decay in $k$ was only known for the case of XOR and unique games.
• To prove the theorem we extend an analytical framework recently introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition.