Exponential all-win parallel repetition for entangled games
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Does the probability of winning all n independent repetitions of a finite two-player entangled game decay exponentially whenever its entangled value is below one? The target permits arbitrary finite games, with decay depending on the value gap and answer alphabets.
Why it matters and what counts as progress
Why it matters: Entangled strategies correlate repetitions in ways that prevent classical parallel-repetition bounds from applying automatically.
What counts as progress: Prove exponential all-win repetition without special question-distribution assumptions or improve the dependence of the exponent on game parameters.
How the problem developed
- 23 Aug 2016 · Polynomial parallel repetition [1]
Henry Yuen Proved polynomial decay of the entangled value under repetition for every finite two-player game whose entangled value is below one, giving convergence to zero but not exponential decay for arbitrary games.
- 25 Sept 2026 · Exponential threshold repetition [2]
OpenAI Reported exponential decay in the probability of winning at least a v+δ fraction of repetitions for any finite two-player game of finite-dimensional entangled value v<1; all-win repetition is the special threshold 1 case.
AI contribution
Ten Advances in Mathematics and Theoretical Computer Science
For every finite two-player entangled game G with entangled value below one, the value of winning all n independent repetitions decays exponentially in n; the Chapter 6 bound depends on the gap and answer alphabet sizes.
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