[Paper Review] QMIP = MIP*

Anne Broadbent, Joseph F. Fitzsimons+1 more|arXiv (Cornell University)|Apr 7, 2010

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper proves that QMIP, the class of languages decidable by quantum multi-prover interactive proof systems, is equal to MIP*, the class of languages decidable by classical multi-prover systems with entangled provers. By adapting universal blind quantum computation to the interactive proof framework, the authors show that shared entanglement alone captures the full power of quantum advantage in this setting, eliminating the need for a quantum verifier.

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.

Motivation & Objective

• To resolve the long-standing open question of whether quantum multi-prover interactive proof systems (QMIP) are more powerful than classical ones with entangled provers (MIP*).
• To determine whether quantum communication or shared entanglement is the key resource for quantum advantage in multi-prover proof systems.
• To show that a classical verifier can achieve the same computational power as a quantum verifier when provers share entanglement.
• To establish that the entire power of quantum information in this setting is captured by entanglement, not by quantum communication or quantum verification.

Proposed method

• Adapting the universal blind quantum computation protocol to the multi-prover interactive proof model.
• Using shared entanglement to simulate quantum computation in a way that allows a classical verifier to delegate quantum computation securely.
• Constructing a protocol where entangled provers can simulate any quantum computation without requiring the verifier to perform quantum operations.
• Demonstrating that the verifier’s quantum capabilities are unnecessary when provers share entanglement, by reducing quantum verification to classical verification with entangled provers.
• Leveraging the structure of interactive proofs to show that entanglement enables universal quantum computation in the MIP* framework.
• Proving that the resulting system achieves the same expressive power as QMIP, thereby establishing QMIP = MIP*.

Experimental results

Research questions

• RQ1 Is a quantum verifier necessary for the full power of quantum multi-prover interactive proof systems, or can a classical verifier suffice with entangled provers?
• RQ2 Does shared entanglement alone provide the full computational advantage of quantum information in multi-prover proof systems?
• RQ3 Can universal quantum computation be delegated to entangled provers using only classical interaction with a classical verifier?
• RQ4 What is the precise role of entanglement versus quantum communication in enhancing the power of interactive proof systems?
• RQ5 Is the class QMIP strictly larger than MIP*, or are they equivalent?

Key findings

• QMIP is exactly equal to MIP*, meaning that quantum multi-prover interactive proof systems do not offer more computational power than classical systems with entangled provers.
• The entire power of quantum information in this context is captured by shared entanglement, not by quantum communication or quantum verification.
• A classical verifier can simulate any quantum verifier in the multi-prover setting when the provers share entanglement.
• Universal blind quantum computation can be adapted to interactive proof systems to achieve full quantum computational universality using only classical interaction.
• The result implies that quantum advantage in this model arises solely from entanglement, not from the verifier’s quantum capabilities.
• The proof establishes a tight equivalence between quantum and entangled classical proof systems, completing the picture from the verifier’s perspective.