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Entangled parallel repetition conjecture

Let GG be any finite two-player, one-round entangled game with entangled value ω∗(G)=1−ε<1\omega^*(G)=1-\varepsilon<1. The conjecture asserts that there exists a constant c=c(G)>0c=c(G)>0 such that, for every integer n≥1n\ge 1, the entangled value of the nn-fold parallel repetition satisfies ω∗(G⊗n)≤e−cn\omega^*(G^{\otimes n})\le e^{-cn}.

Progress summary

Solved

A 2026 manuscript claims the conjecture is solved, but an audit has repaired only a local step and has not confirmed the main theorem.

The conjecture asks for exponential decay under parallel repetition for every finite two-player entangled game. General convergence to zero is known, but the claimed exponential bound remains the decisive issue.

Known results

  • Kempe, Regev, and Toner (2009): strong parallel repetition fails for entangled games, without refuting ordinary convergence.
  • Yuen (2016): for arbitrary games, repeated value tends to zero with a polynomial bound, not exponentially.
  • Bavarian, Vidick, and Yuen (2013): exponential decay for entangled projection games.
  • Anchoring results (2013–2015): exponential decay for product-distribution and anchored games.

August 2026 claimed proof and audit

An OpenAI manuscript and a preprint dated August 2026 claim exponential decay for all finite two-player entangled games, with the preprint improving the stated gap dependence. The August audit repairs a local proof error and reports that the lemma survives, but explicitly does not validate the downstream argument or central theorem.

Current status (as of August 2026): Polynomial decay for arbitrary games and exponential decay in special cases are established, while the general exponential conjecture is only claimed in an unverified manuscript and remains open.

Sources
Sources & referencesView supporting material

Primary source

arXiv

Additional references

proof-auditingquantum-informationtheoretical-computer-science

Solutions 0

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