QMA(2) with Limited Shared Entanglement

2026-10-15 · arXiv Quantum Physics

arXiv:2609.39668v3 Announce Type: replace

Abstract: In $\mathsf{QMA}(2)$, two computationally unbounded provers submit unentangled quantum witnesses to a polynomial-time quantum verifier. We ask whether allowing limited shared entanglement between the two provers changes the power of $\mathsf{QMA}(2)$. To this end, we formalize $\mathsf{QMA}(2;h)$, a variant in which the provers initially share $h$ EPR pairs, as suggested by Aaronson, Beigi, Drucker, Fefferman, and Shor (ToC~2009). We show that polynomially many shared EPR pairs give the provers no cheating advantage: $\mathsf{QMA}(2)\subseteq\mathsf{QMA}(2;h)$ for $h=\operatorname{poly}(n)$. For logarithmically many pairs, the power of $\mathsf{QMA}(2)$ remains unchanged, strengthening this inclusion to $\mathsf{QMA}(2)=\mathsf{QMA}(2;h)$ for $h=O(\log n)$. Finally, we introduce a variant that also allows classical communication between the provers when preparing the witnesses. This setting is particularly revealing for logarithmic-size witnesses: assuming $\mathsf{NP}\nsubseteq\mathsf{BQP}$, we show that superlogarithmically many shared EPR pairs strictly reduce the model's computational power.

原文链接：https://arxiv.org/abs/2609.39668

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