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OP-6909Status unassessedQuantum information

Uniform Exponential Quantum Parallel Repetition

TheoremDB P3566 · quantum information

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓
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Problem statement

Prove that there is a universal constant c>0c>0 such that every finite two-player quantum game GG with nonempty answer sets A,BA,B and gap δ=1−ω∗(G)>0\delta=1-\omega^*(G)>0 satisfies ω∗(G⊗n)≤exp⁡(−cδ13n/(δ+log⁡(∣A∣∣B∣)))\omega^*(G^{\otimes n})\le\exp(-c\delta^{13}n/(\delta+\log(|A||B|))) for every integer n≥1n\ge1.

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Formal statement

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theorem QuantumParallelRepetition.distributionUniformExponential : ∃ c : ℝ, 0 < c ∧ ∀ {X Y A B : Type} [Fintype X] [Fintype Y] [Fintype A] [Fintype B] (G : Game X Y A B), Nonempty A → Nonempty B → 0 < 1 - entangledValue G → ∀ n : ℕ, 0 < n → repeatedEntangledValue G n ≤ Real.exp (-(c * ((1 - entangledValue G) ^ 13 / ((1 - entangledValue G) + Real.log ((Fintype.card A : ℝ) * (Fintype.card B : ℝ))))) * (n : ℝ))

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Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

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References
  1. [1]TheoremDB P3566 link
  2. [2]Source formal statement (not locally verified) link

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Discussion

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