Threshold parallel repetition for finite-dimensional entangled games
For every finite two-player game with entangled value v < 1, we prove exponential decay for the probability of winning at least a $v+\delta$ fraction of k independent repetitions, uniformly over all finite-dimensional joint strategies. The result allows arbitrary correlated question distributions and holds for every $0\lt \delta\lt 1-v$ and k ≥ 1. Its universal rate is proportional to $\delta^5/(1+\log(|\mathcal A||\mathcal B|))$, where $\mathcal A,\mathcal B$ are the answer alphabets. For each fixed question distribution, we also obtain an explicit cubic rate in δ .
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