Quantum Interactive Proofs with Competing Provers

TL;DR

This paper introduces quantum refereed games with two competing provers, demonstrating that such games can simulate standard quantum interactive proofs with minimal communication, and explores error reduction techniques.

Contribution

It proves that all languages with quantum interactive proofs also have equivalent quantum refereed games with one round of exchange, and introduces a measurement technique for distinguishing quantum states.

Findings

Quantum refereed games can simulate quantum interactive proofs.

Existence of a single measurement to distinguish mixed states from disjoint convex sets.

Error probability can be reduced in certain quantum refereed games.

Abstract

This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that every language having an ordinary quantum interactive proof system also has a quantum refereed game in which the verifier exchanges just one round of messages with each prover. A key part of our proof is the fact that there exists a single quantum measurement that reliably distinguishes between mixed states chosen arbitrarily from disjoint convex sets having large minimal trace distance from one another. We also show how to reduce the probability of error for some classes of quantum refereed games.