Communication complexity bounds from information causality

TL;DR

This paper develops an information-theoretic framework using mutual information to derive bounds on communication complexity, extending the principle of information causality and linking it to quantum correlations in Bell experiments.

Contribution

It introduces an axiomatic approach to one-way communication complexity and extends the information causality principle to derive new bounds and insights into quantum correlations.

Findings

Extended information causality recovers known communication bounds.

New bounds on quantum correlations in Bell experiments.

Framework simplifies analysis of quantum communication limits.

Abstract

Communication complexity, which quantifies the minimum communication required for distributed computation, offers a natural setting for investigating the capabilities and limitations of quantum mechanics in information processing. We introduce an information-theoretic approach to study one-way communication complexity based solely on the axioms of mutual information. Within this framework, we derive an extended statement of the information causality principle, which recovers known lower bounds on the communication complexities for a range of functions in a simplified manner and leads to new results. We further prove that the extended information causality principle is at least as strong as the principle of non-trivial communication complexity in bounding the strength of quantum correlations attainable in Bell experiments. Our study establishes a new route for exploring the fundamental limits of quantum technologies from an information-theoretic viewpoint.