In a two player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution.
Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs.
The entangled value ω*(G) of a game G is the maximum probability that Alice and Bob can win the game if they are allowed to share an entangled state prior to receiving their inputs.
The n-fold parallel repetition G^n of G consists of n instances of G where Alice and Bob receive all the inputs at the same time and must produce all the outputs at the same time. They win G^n if they win each instance of G.
Here we show that for any game G such that ω*(G) = 1−ε < 1, ω*(G^n) decreases exponentially in n.
To prove this parallel repetition, we introduce the concept of Superposed Information Cost for entangled games which is inspired from the information cost used in communication complexity.