Coherent state exchange in multi-prover quantum interactive proof systems

TL;DR

This paper demonstrates that parties can coherently exchange quantum states without communication using shared entanglement, and applies this to show limitations and improvements in multi-prover quantum interactive proof systems.

Contribution

It introduces a method for coherent state exchange in multi-party quantum systems and applies it to analyze and enhance multi-prover quantum proof protocols.

Findings

No finite entanglement allows optimal strategy in certain proof systems

Provers can approach near-certain acceptance with unbounded entanglement

Multi-prover proofs can be made near-perfect with one additional round of communication

Abstract

We show that any number of parties can coherently exchange any one pure quantum state for another, without communication, given prior shared entanglement. Two applications of this fact to the study of multi-prover quantum interactive proof systems are given. First, we prove that there exists a one-round two-prover quantum interactive proof system for which no finite amount of shared entanglement allows the provers to implement an optimal strategy. More specifically, for every fixed input string, there exists a sequence of strategies for the provers, with each strategy requiring more entanglement than the last, for which the probability for the provers to convince the verifier to accept approaches 1. It is not possible, however, for the provers to convince the verifier to accept with certainty with a finite amount of shared entanglement. The second application is a simple proof that multi-prover quantum interactive proofs can be transformed to have near-perfect completeness by the addition of one round of communication.