QMIP = MIP*

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. Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada. Department of Materials, University of Oxford, Oxford, United Kingdom. School of Informatics, University of Edinburgh, Edinburgh, Scotland, United Kingdom. ∗Email: albroadb@iqc.ca, joe.fitzsimons@materials.ox.ac.uk, ekashefi@inf.ed.ac.uk ar X iv :1 00 4. 11 30 v1 [ qu an tph ] 7 A pr 2 01 0