Towards a quantum-inspired proof for IP = PSPACE

We explore quantum-inspired interactive proof systems where the prover is limited. Namely, we improve on a result by [AG17] showing a quantum-inspired interactive protocol ($\sf IP$) for $\sf PreciseBQP$ where the prover is only assumed to be a $\sf PreciseBQP$ machine, and show that the result can be strengthened to show an $\sf IP$ for $\sf NP^{PP}$ with a prover which is only assumed to be an $\sf NP^{PP}$ machine - which was not known before. We also show how the protocol can be used to directly verify $\sf QMA$ computations, thus connecting the sum-check protocol by [AAV13] with the result of [AG17, LFKN90]. Our results shed light on a quantum-inspired proof for ${\sf IP} = {\sf PSPACE}$, as $\sf PreciseQMA$ captures the full $\sf PSPACE$ power.