Quantum Merlin-Arthur with an internally separable proof

Abstract: We find a modification to QMA where having one quantum proof is strictly less powerful than having two unentangled proofs, assuming EXP $\ne$ NEXP. This gives a new route to prove QMA(2) = NEXP that overcomes the primary drawback of a recent approach arXiv:2402.18790 , arXiv:2306.13247. Our modification endows each proof with a form of multipartite unentanglement: after tracing out one register, a small number of qubits are separable from the rest of the state.