Continuous input nonlocal games

TL;DR

This paper introduces a family of nonlocal games with continuous inputs, demonstrating quantum advantage in some cases and conjecturing it in others, expanding understanding of quantum correlations in nonlocal games.

Contribution

The paper presents a new family of nonlocal games with continuous inputs and analyzes quantum versus classical correlations, including a conjecture for the general case.

Findings

Quantum advantage shown in two game members

Classical correlations are outperformed by quantum in these cases

Conjecture that quantum advantage extends to the third game member

Abstract

We present a family of nonlocal games in which the inputs the players receive are continuous. We study three representative members of the family. For the first two a team sharing quantum correlations (entanglement) has an advantage over any team restricted to classical correlations. We conjecture that this is true for the third member of the family as well.