The relation between the quantum games, communication complexity problems and Bell inequalities

TL;DR

This paper explores the connections between quantum games, communication complexity problems, and Bell inequalities, revealing cases where these relationships do not hold and highlighting quantum advantages in certain problems.

Contribution

It demonstrates that not all elements of these groups are related and shows that quantum strategies outperform classical ones when Bell inequalities are absent.

Findings

Some elements lack correspondence across the groups.

Quantum strategies have higher advantage without Bell inequalities.

Identifies cases where relations between the concepts do not exist.

Abstract

We study the relation between the quantum games, communication complexity problems and Bell inequalities. In particular we are interested in answering the question whether for every element of one of these groups there is a corresponding element in the other two. We show that there are cases where there is no such relation. Moreover, in the communication complexity problems for which there is no Bell inequality the advantage of the quantum strategies over the classical ones is much higher.