Entanglement in Interactive Proof Systems with Binary Answers

TL;DR

This paper demonstrates that when two entangled provers answer binary questions with XOR, the proof system's power is limited to that of a single quantum prover, contrasting with the classical case where two provers are more powerful.

Contribution

It proves that +MIP*[2] with XOR answers is contained in QIP(2), showing entanglement does not increase proof system power in this setting.

Findings

+MIP*[2] is contained in QIP(2).

+MIP*[2] is contained in EXP.

Entanglement does not enhance proof system power with XOR answers.

Abstract

If two classical provers share an entangled state, the resulting interactive proof system is significantly weakened [quant-ph/0404076]. We show that for the case where the verifier computes the XOR of two binary answers, the resulting proof system is in fact no more powerful than a system based on a single quantum prover: +MIP*[2] is contained in QIP(2). This also implies that +MIP*[2] is contained in EXP which was previously shown using a different method [Presentation of Cleve et al. at CCC'04]. This contrasts with an interactive proof system where the two provers do not share entanglement. In that case, +MIP[2] = NEXP for certain soundness and completeness parameters [quant-ph/0404076].