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 $k\ge1$. 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 $\delta$.