Worst to average case reductions for quantum complexity classes

I am studying worst to average case reductions for different complexity classes.

Consider quantum complexity classes like QMA, QSZK, or QIP. Is it known or believed that these classes are amenable to worst-to-average-case reductions?

• QIP=PSPACE, so "yes". QMA seems very analogous NP, so "probably not". Dec 6 '21 at 0:44
• What about QSZK? Dec 9 '21 at 4:53