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Threshold repetition for entangled games

Proves exponential threshold repetition for every finite two-player one-round game: if its entangled value is v < 1, the probability of winning at least a fraction

v+\delta

of k independent repetitions decays exponentially in k, for

0\lt \delta\lt 1-v

. Arbitrary joint finite-dimensional entangled strategies and correlated question distributions are allowed.

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Threshold parallel repetition for finite-dimensional entangled games

Sep 25, 2026·paper.pdfLean

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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