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.