Quantum Multiprover Interactive Proofs with Communicating Provers

We introduce a new variant of quantum multiprover interactive proofs (QMIP) where the provers and the verifier are quantum. The verifier can exchange quantum messages with the provers. The provers cannot communicate quantumly between themselves and do not share entanglement, but are unlimited in the classical communication between them, even after receiving messages from the verifier. We show that any language in nondeterministic exponential time (NEXP) can be recognized in this model efficiently, with just two provers and two rounds of communication, and with a constant completeness/soundness gap. This is in contrast to the result of [R. Jain et al., Comm. ACM, 53 (2010), pp. 102--109], which shows that QIP = PSPACE, or equivalently that the set of languages that can be recognized by a quantum verifier communicating with a single quantum prover is equal to PSPACE. To analyze the cheating power of the provers, we give them more power and allow them to perform any separable operation. We then show a unique...