发表机构
Boston University; Georgetown University（波士顿大学; 乔治城大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究 QMA 中批量验证布尔函数\(f\)的资源与副本数量关系，给出依近似度证下限的通用技术，应用于 DNF 公式族，得出节省见证长度会致查询成本大增，还获 CNF 公式等的 QMA 查询复杂性下限及通信类似结果。
AI 中文摘要
我们研究量子 Merlin - Arthur（QMA）查询和通信复杂性中的批量验证，目标是了解验证布尔函数\(f\)的\(m\)个副本所需资源如何依赖于\(m\)。我们给出一种通用技术，用于根据近似度证明批量验证函数\(f\)所需见证查询权衡的下限。将此技术应用于显式的析取范式（DNF）公式族\(f\)，表明即使在批量验证\(f\)的基线方法的见证长度上节省常数因子，也需要查询成本大幅多项式增加。我们还获得了一次读取合取范式（CNF）公式的 QMA 查询复杂性以及满射性和\(k\)元互异性函数的新下限。我们的下限还可提升以给出这些结果的通信类似物。
英文摘要
We study batch verification in QMA query and communication complexity, where the goal is to understand how the resources needed to verify $m$ copies of a Boolean function $f$ depend on $m$. We give a general technique for proving lower bounds on the witness-query tradeoff needed to batch verify a function $f$ in terms of its approximate degree. Applying this technique to an explicit family of DNF formulas $f$, we show that attempting to save even a constant factor on the witness length of the baseline approach to batch verifying $f$ necessitates a large polynomial increase in the query cost. We also obtain new lower bounds on the QMA query complexity of read-once CNF formulas and on the surjectivity and $k$-element distinctness functions. Our lower bounds also lift to give communication analogs of these results.
CommentsA conference version of this paper was published at RANDOM 2026
DOI：10.4230/LIPIcs.APPROX/RANDOM.2026.69
