  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.
