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 the connection between unitary property testing and unitary channel discrimination. The main advantage of this technique is that all obtained lower bounds hold for any $\mathsf{C}$-tester with $\mathsf{C} \subseteq \mathsf{QMA}(\text{poly(n)} / \mathsf{qpoly}$, 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 exists a quantum oracle relative to which $\mathsf{QMA}(\text{poly(n)} / \mathsf{qpoly} \not\supset \mathsf{SBQP}$.

翻译：在酉性质测试中，量子算法（称为测试器）通过黑盒酉操作进行查询访问，需判断其是否满足特定性质。我们提出一种新方法，用于证明酉性质测试及相关问题的量子查询复杂度下界，该方法利用了酉性质测试与酉信道判别之间的联系。该技术的主要优势在于：所有获得的下界对任意满足 $\mathsf{C} \subseteq \mathsf{QMA}(\text{poly(n)} / \mathsf{qpoly}$ 的 $\mathsf{C}$-测试器均成立，表明即使拥有（非纠缠）量子证明和建议访问权限，对许多酉问题仍无帮助。我们将该技术应用于证明量子相位估计、纠缠熵问题、量子吉布斯采样等问题的下界，消除了Wang与Zhang（2023）样本到查询提升定理所获下界中的全部对数因子。作为直接推论，我们证明存在一个量子谕示，使得 $\mathsf{QMA}(\text{poly(n)} / \mathsf{qpoly} \not\supset \mathsf{SBQP}$。