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 $0<\delta <1-v$ 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.