Quantum communication complexity advantage implies violation of a Bell inequality

TL;DR

This paper establishes a fundamental link between quantum communication advantages and non-local correlations, showing that significant quantum advantages imply violations of Bell inequalities, thus connecting quantum communication complexity with quantum non-locality.

Contribution

It demonstrates that any quantum protocol with a large advantage in communication complexity can be used to generate measurement statistics that violate Bell inequalities, using port-based teleportation.

Findings

Quantum advantage in communication complexity implies Bell inequality violation.

The ratio of quantum to classical Bell values can become unbounded with increasing inputs and outputs.

Port-based teleportation is a key tool in establishing this connection.

Abstract

We obtain a general connection between a quantum advantage in communication complexity and non-locality. We show that given any protocol offering a (sufficiently large) quantum advantage in communication complexity, there exists a way of obtaining measurement statistics which violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily large, the ratio of the quantum value to the classical value of the Bell quantity becomes unbounded with the increase in the number of inputs and outputs.