Using Entanglement in Quantum Multi-Prover Interactive Proofs

TL;DR

This paper explores how shared entanglement among provers in quantum multi-prover interactive proof systems can enhance their power, enabling parallelization and maintaining perfect completeness, which contrasts classical limitations.

Contribution

It demonstrates for the first time that entanglement can be beneficial for honest provers, allowing parallelization of proof systems with minimal rounds and public-coin properties.

Findings

Entanglement enables parallelization of quantum proof systems.

Shared entanglement maintains perfect completeness in proof systems.

Public-coin property achieved with entanglement contrasts classical results.

Abstract

The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared between provers affects the verification power of the proof system. We study for the first time positive aspects of prior entanglement and show that entanglement is useful even for honest provers. We show how to use shared entanglement to parallelize any multi-prover quantum interactive proof system to a one-round system with perfect completeness, with one extra prover. Alternatively, we can also parallelize to a three-turn system with the same number of provers, where the verifier only broadcasts the outcome of a coin flip. This "public-coin" property is somewhat surprising, since in the classical case public-coin multi-prover interactive proofs are equivalent to single prover ones.