Towards a quantum-inspired proof for IP = PSPACE

Abstract

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