A Parallel Repetition Theorem for Entangled Two-player One-round Games Under Product Distributions
summary
For entangled two-player one-round games with a product input distribution the k-fold parallel repetition lowers the maximum winning probability exponentially in k: the value of G^k is at most (value of G + small epsilon)^{Omega(k)}. The proof conditions on success on some coordinates, finds coordinates whose conditional win probability is bounded away from one by unitary embedding avoids measurement, uses low mutual information to construct local unitaries, and iterates this argument value decays exponentially.
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