Entanglement-Resistant Two-Prover Interactive Proof Systems and Non-Adaptive Private Information Retrieval Systems

TL;DR

This paper introduces an entanglement-resistant two-prover interactive proof system for NP languages with constant bits and a constant gap, leveraging private information retrieval systems, advancing the understanding of quantum-resistant proof protocols.

Contribution

It presents the first entanglement-resistant constant-bit two-prover proof system with a constant gap for NP, using novel private information retrieval techniques.

Findings

Achieves entanglement resistance in two-prover systems

Establishes a constant completeness vs. soundness gap

Introduces an oracular property of private information retrieval systems

Abstract

We show that, for any language in NP, there is an entanglement-resistant constant-bit two-prover interactive proof system with a constant completeness vs. soundness gap. The previously proposed classical two-prover constant-bit interactive proof systems are known not to be entanglement-resistant. This is currently the strongest expressive power of any known constant-bit answer multi-prover interactive proof system that achieves a constant gap. Our result is based on an "oracularizing" property of certain private information retrieval systems, which may be of independent interest.