Non-Locality in Interactive Proofs

TL;DR

This paper explores how non-locality affects multi-prover interactive proofs by introducing a generalized model that accounts for verifier contamination and reveals new properties like zero-knowledge.

Contribution

It formalizes the verifier contamination problem and extends the MIP model to include non-locality as a key dimension, offering new insights into proof properties.

Findings

Verifier contamination is a fundamental issue in MIPs.

A generalized MIP model incorporating non-locality is proposed.

Zero-knowledge properties naturally emerge from the non-locality framework.

Abstract

In multi-prover interactive proofs (MIPs), the verifier is usually non-adaptive. This stems from an implicit problem which we call ``contamination'' by the verifier. We make explicit the verifier contamination problem, and identify a solution by constructing a generalization of the MIP model. This new model quantifies non-locality as a new dimension in the characterization of MIPs. A new property of zero-knowledge emerges naturally as a result by also quantifying the non-locality of the simulator.