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 MIP = NEXP 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-亚瑟协议）的变体，其中亚瑟除了可以执行普通塌缩测量外，还能对梅林的见证态进行多次非塌缩测量。类比于Aaronson、Bouland、Fitzsimons和Lee（2014）定义的PDQP类，我们将此类称为PDQMA。我们的主要结果是PDQMA = NEXP；这一结论建立在MIP = NEXP定理之上，并补充了Aaronson（2018）的结果：PDQP/qpoly = ALL。尽管该结果与量子力学关联不大，但我们还展示了一个更“量子化”的结果：即在关于隐藏变量理论的温和假设下，QMA若具备检查隐藏变量完整历史的能力，则等价于NEXP。我们还观察到，一台配备量子建议并能检查隐藏变量历史的量子计算机，可以在多项式时间内解决任何判定问题。