Parallel Repetition for Entangled Games via Conditional Relative Entropy

@misc{jain2026parallel,
  title = {{Parallel Repetition for Entangled Games via Conditional Relative Entropy}},
  author = {Rahul Jain},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21410},
  eprint = {2610.21410},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21410},
}

TY  - UNPB
TI  - Parallel Repetition for Entangled Games via Conditional Relative Entropy
AU  - Rahul Jain
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21410
UR  - https://arxiv.org/abs/2610.21410
AB  - We give a proof of the cubic parallel-repetition bound for finite two-player entangled games using quantum conditional relative entropy. For a game with entangled value 1−ε<1 and answer alphabets 𝒜,ℬ, its n-fold repeated value is at most exp[−Ω(ε^3n/L)], L:=max{1,log(|𝒜||ℬ|)}, for every n≥1. This recovers Song's cubic rate. We also prove a threshold bound: the probability of winning a fraction at least 1−ε+δ is at most exp[−Ω(δ^5n/(ε^2L))] for 0<δ≤ε. Our information charge is the decrease in relative entropy when a question reference is discarded. Our comparison states preserve the original conditional question law. A chain rule bounds the coordinate charges using the cost of conditioning on checked wins and retaining checked answers. Our main lemma converts small charges into nearby pure-state descriptions and local corrections, each depending only on one player's question. Together with Song's sampler, these enable approximate local preparation of the conditioned workspace.
ER  -