In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum query complexity of unitary property testing and related problems, which utilises its connection to unitary channel discrimination. The main advantage of this technique is that all obtained lower bounds hold for any $\mathsf{C}$-tester with $\mathsf{C} \subseteq \mathsf{QMA}(2)/\mathsf{qpoly}$, showing that even having access to both (unentangled) quantum proofs and advice does not help for many unitary problems. We apply our technique to prove lower bounds for problems like quantum phase estimation, the entanglement entropy problem, quantum Gibbs sampling and more, removing all logarithmic factors in the lower bounds obtained by the sample-to-query lifting theorem of Wang and Zhang (2023). As a direct corollary, we show that there exist quantum oracles relative to which $\mathsf{QMA}(2) \not\supset \mathsf{SBQP}$ and $\mathsf{QMA}/\mathsf{qpoly} \not\supset \mathsf{SBQP}$. The former shows that, at least in a black-box way, having unentangled quantum proofs does not help in solving problems that require high precision.

翻译：在酉性质测试中，量子算法（也称为测试者）通过查询访问黑盒酉算子，并需要判断其是否满足某种性质。我们提出了一种新技术，用于证明酉性质测试及相关问题的量子查询复杂性的下界，该技术利用了其与酉信道区分的联系。该技术的主要优势在于，所有得到的下界对任何$\mathsf{C}$-测试者（其中$\mathsf{C} \subseteq \mathsf{QMA}(2)/\mathsf{qpoly}$）均成立，表明即使拥有（非纠缠的）量子证明和辅助，对许多酉问题也无帮助。我们将该技术应用于证明诸如量子相位估计、纠缠熵问题、量子吉布斯采样等问题的下界，去除了Wang和Zhang（2023）的样本到查询提升定理所得到下界中的所有对数因子。作为直接推论，我们证明了存在量子神谕使得$\mathsf{QMA}(2) \not\supset \mathsf{SBQP}$且$\mathsf{QMA}/\mathsf{qpoly} \not\supset \mathsf{SBQP}$。前者表明，至少在黑盒方式下，拥有非纠缠量子证明对解决需要高精度的问题并无帮助。