QMIP = MIP*

TL;DR

This paper proves that the class of languages recognized by quantum multi-prover interactive proof systems (QMIP) is equal to the class recognized by classical systems with shared entanglement (MIP*), showing shared entanglement captures all quantum power in this setting.

Contribution

It establishes QMIP=MIP*, demonstrating shared entanglement suffices to replicate quantum proof system power without quantum verifiers.

Findings

QMIP equals MIP*

Shared entanglement removes the need for quantum verifiers

Quantum information power is captured by entanglement

Abstract

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.