We define and study a variant of QMA (Quantum Merlin Arthur) in which Arthur can make multiple non-collapsing measurements to Merlin's witness state, in addition to ordinary collapsing measurements. By analogy to the class PDQP defined by Aaronson, Bouland, Fitzsimons, and Lee (2014), we call this class PDQMA. Our main result is that PDQMA = NEXP; this result builds on the PCP theorem and complements the result of Aaronson (2018) that PDQP/qpoly = ALL. While the result has little to do with quantum mechanics, we also show a more "quantum" result: namely, that QMA with the ability to inspect the entire history of a hidden variable is equal to NEXP, under mild assumptions on the hidden-variable theory. We also observe that a quantum computer, augmented with quantum advice and the ability to inspect the history of a hidden variable, can solve any decision problem in polynomial time.

翻译：我们定义并研究了一种QMA（量子梅林-亚瑟证明系统）的变体，其中亚瑟除了可以进行普通的坍缩测量外，还能对梅林的见证态进行多次非坍缩测量。类比于Aaronson、Bouland、Fitzsimons和Lee（2014年）定义的PDQP类，我们将此类称为PDQMA。我们的主要结果是PDQMA = NEXP；该结果建立在PCP定理的基础上，并与Aaronson（2018年）证明的PDQP/qpoly = ALL这一结论形成互补。尽管该结果与量子力学关系不大，我们还证明了一个更具“量子性”的结论：即在关于隐变量理论的温和假设下，具备检查隐变量完整历史能力的QMA等于NEXP。我们还观察到，一台量子计算机若辅以量子建议态以及检查隐变量历史的能力，则可在多项式时间内解决任何判定问题。