  The way entanglement influences the power of quantum and classical
multi-prover interactive proof systems is a long-standing open question. We
show that the class of languages recognized by quantum multi-prover interactive
proof systems, QMIP, is equal to MIP*, the class of languages recognized by
classical multi-prover interactive proof systems where the provers share
entanglement. After the recent result by Jain, Ji, Upadhyay and Watrous showing
that QIP=IP, our work completes the picture from the verifier's perspective by
showing that also in the setting of multiple provers with shared entanglement,
a quantum verifier is no more powerful than a classical one: QMIP=MIP*. Our
techniques are based on the adaptation of universal blind quantum computation
(a protocol recently introduced by us) to the context of interactive proof
systems. We show that in the multi-prover scenario, shared entanglement has a
positive effect in removing the need for a quantum verifier. As a consequence,
our results show that the entire power of quantum information in multi-prover
interactive proof systems is captured by the shared entanglement and not by the
quantum communication.
