Quantum Advantage from Any Non-Local Game

TL;DR

This paper introduces a method to convert any multi-prover non-local game into a single-prover interactive game using quantum homomorphic encryption, enabling classical verification of quantum advantage.

Contribution

It presents a general compiler that transforms k-prover non-local games into single-prover games while preserving key quantum and classical guarantees, leveraging quantum homomorphic encryption.

Findings

Enables classical verification of quantum advantage.

Provides a broad framework for constructing quantum non-local game-based mechanisms.

Maintains completeness and soundness guarantees in the transformation.

Abstract

We show a general method of compiling any $k$-prover non-local game into a single-prover interactive game maintaining the same (quantum) completeness and (classical) soundness guarantees (up to negligible additive factors in a security parameter). Our compiler uses any quantum homomorphic encryption scheme (Mahadev, FOCS 2018; Brakerski, CRYPTO 2018) satisfying a natural form of correctness with respect to auxiliary (quantum) input. The homomorphic encryption scheme is used as a cryptographic mechanism to simulate the effect of spatial separation, and is required to evaluate $k-1$ prover strategies (out of $k$) on encrypted queries. In conjunction with the rich literature on (entangled) multi-prover non-local games starting from the celebrated CHSH game (Clauser, Horne, Shimonyi and Holt, Physical Review Letters 1969), our compiler gives a broad framework for constructing mechanisms to classically verify quantum advantage.