Extended Nonlocal Games from Quantum-Classical Games

TL;DR

This paper introduces a method to construct extended nonlocal games from quantum-classical games, simplifying proofs of the non-existence of finite-dimensional optimal strategies and potentially aiding future research in quantum entanglement.

Contribution

It provides a new construction linking quantum-classical and extended nonlocal games, simplifying existing proofs and opening avenues for further applications.

Findings

Existence of extended nonlocal games with no finite-dimensional optimal strategies.

Simplified proof approach based on the construction.

Potential applications in entanglement and nonlocality studies.

Abstract

Several variants of nonlocal games have been considered in the study of quantum entanglement and nonlocality. This paper concerns two of these variants, called quantum-classical games and extended nonlocal games. We give a construction of an extended nonlocal game from any quantum-classical game that allows one to translate certain facts concerning quantum- classical games to extended nonlocal games. In particular, based on work of Regev and Vidick, we conclude that there exist extended nonlocal games for which no finite-dimensional entangled strategy can be optimal. While this conclusion is a direct consequence of recent work of Slofstra, who proved a stronger, analogous result for ordinary (non-extended) nonlocal games, the proof based on our construction is considerably simpler, and the construction itself might potentially have other applications in the study of entanglement and nonlocality.