{"id":"openai-math/Threshold-parallel-repetition-for-finite-dimensional-entangled-games","pdf":"https://github.com/openai/math/blob/main/preprints/Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Threshold-parallel-repetition-for-finite-dimensional-entangled-games-September-25-2026","tags":["quantum-information","entangled-games","parallel-repetition"],"score":0,"title":"Threshold parallel repetition for finite-dimensional entangled games","domain":"Mathematical physics","family":"277","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"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 .","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"family_title":"Threshold repetition for entangled games"}