Stoquasticity, originating in sign-problem-free physical systems, gives rise to $\sf StoqMA$, introduced by Bravyi, Bessen, and Terhal (2006), a quantum-inspired intermediate class between $\sf MA$ and $\sf AM$. Unentanglement similarly gives rise to ${\sf QMA}(2)$, introduced by Kobayashi, Matsumoto, and Yamakami (CJTCS 2009), which generalizes $\sf QMA$ to two unentangled proofs and still has only the trivial $\sf NEXP$ upper bound. In this work, we initiate a systematic study of the power of unentanglement without destructive interference via ${\sf StoqMA}(2)$, the class of unentangled stoquastic Merlin-Arthur proof systems. Although $\sf StoqMA$ is semi-quantum and may collapse to $\sf MA$, ${\sf StoqMA}(2)$ turns out to be surprisingly powerful. We establish the following results: - ${\sf NP} \subseteq {\sf StoqMA}(2)$ with $\widetilde{O}(\sqrt{n})$-qubit proofs and completeness error $2^{-{\rm polylog}(n)}$. Conversely, ${\sf StoqMA}(2) \subseteq {\sf EXP}$ via the Sum-of-Squares algorithm of Barak, Kelner, and Steurer (STOC 2014); with our lower bound, our refined analysis yields the optimality of this algorithm under ETH. - ${\sf StoqMA}(2)_1 \subseteq {\sf PSPACE}$, and the containment holds with completeness error $2^{-2^{{\rm poly}(n)}}$. - ${\sf PreciseStoqMA}(2)$, a variant of ${\sf StoqMA}(2)$ with exponentially small promise gap, cannot achieve perfect completeness unless ${\sf EXP}={\sf NEXP}$. In contrast, ${\sf PreciseStoqMA}$ achieves perfect completeness, since ${\sf PSPACE} \subseteq {\sf PreciseStoqMA}_1$. - When the completeness error is negligible, ${\sf StoqMA}(k) = {\sf StoqMA}(2)$ for $k\geq 2$. Our lower bounds are obtained by stoquastizing the short-proof ${\sf QMA}(2)$ protocols via distribution testing techniques. Our upper bounds for the nearly perfect completeness case are proved via our new rectangular closure testing framework.

翻译：随机无符号性（Stoquasticity）源于无符号问题物理系统，由Bravyi、Bessen和Terhal（2006）引入$\sf StoqMA$类，这是介于$\sf MA$和$\sf AM$之间的一种量子启发式中间类。无纠缠性同样催生了由Kobayashi、Matsumoto和Yamakami（CJTCS 2009）提出的${\sf QMA}(2)$类，它将$\sf QMA$推广至两个无纠缠证明，且目前仅具有平凡的$\sf NEXP$上界。本文通过${\sf StoqMA}(2)$类（无纠缠随机无符号梅林-亚瑟证明系统）系统研究无相消干涉下无纠缠的威力。尽管$\sf StoqMA$是半量子类且可能坍缩至$\sf MA$，但${\sf StoqMA}(2)$展现出惊人的强大能力。我们建立如下结果： - ${\sf NP} \subseteq {\sf StoqMA}(2)$，使用$\widetilde{O}(\sqrt{n})$量子比特证明，完备性误差为$2^{-{\rm polylog}(n)}$。反之，基于Barak、Kelner和Steurer（STOC 2014）的平方和算法，${\sf StoqMA}(2) \subseteq {\sf EXP}$；结合下界，我们精化的分析证明了该算法在ETH假设下的最优性。 - ${\sf StoqMA}(2)_1 \subseteq {\sf PSPACE}$，且该包含关系在完备性误差为$2^{-2^{{\rm poly}(n)}}$时成立。 - ${\sf PreciseStoqMA}(2)$（${\sf StoqMA}(2)$的变体，具有指数级小承诺间隙）除非${\sf EXP}={\sf NEXP}$，否则无法达到完美完备性。相反，由于${\sf PSPACE} \subseteq {\sf PreciseStoqMA}_1$，${\sf PreciseStoqMA}$可达到完美完备性。 - 当完备性误差可忽略时，对于$k\geq 2$有${\sf StoqMA}(k) = {\sf StoqMA}(2)$。 我们的下界通过分布检验技术对短证明${\sf QMA}(2)$协议进行随机无符号化变换获得。近乎完美完备性情形下的上界则通过我们提出的新矩形闭包检验框架证明。