OpenAI reports threshold repetition for entangled games

For every finite two-player game with finite-dimensional entangled value v<1 and arbitrary correlated questions, the maximum probability of winning at least a fraction v+δ of k repetitions decays at least as exp(−κδ¹³k/(1+log(|A||B|))) for one universal κ>0 and 0<δ<1−v.

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OpenAI reports threshold repetition for entangled games

  • Theoretical Computer Science

For every finite two-player game with finite-dimensional entangled value v<1 and arbitrary correlated questions, the maximum probability of winning at least a fraction v+δ of k repetitions decays at least as exp(−κδ¹³k/(1+log(|A||B|))) for one universal κ>0 and 0<δ<1−v.

AI involvementAI-led
ImportanceMajor
Technical verificationFormal (Lean 4)
Human understandingFew

Understanding the problem

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For every finite two-player game with finite-dimensional entangled value v<1 and arbitrary correlated questions, the maximum probability of winning at least a fraction v+δ of k repetitions decays at least as exp(−κδ¹³k/(1+log(|A||B|))) for one universal κ>0 and 0<δ<1−v.

Why it matters

If correct, gives universal exponential threshold decay for finite-dimensional entangled strategies.

What counts as progress

Does above-value success decay exponentially under parallel repetition of entangled games?

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