Information causality from an entropic and a probabilistic perspective

TL;DR

This paper explores the principle of information causality from entropic and probabilistic viewpoints, relating it to quantum correlations, non-local games, and deriving bounds, aiming for a clearer understanding of its physical and mathematical foundations.

Contribution

It provides a unified analysis of information causality using entropic and probabilistic methods, simplifying its derivation and connecting it to non-local game bounds.

Findings

Quadratic bounds for non-local games derived

Entropic formulation simplifies understanding of information causality

Links between information causality and quantum correlation restrictions

Abstract

The information causality principle is a generalisation of the no-signalling principle which implies some of the known restrictions on quantum correlations. But despite its clear physical motivation, information causality is formulated in terms of a rather specialised game and figure of merit. We explore different perspectives on information causality, discussing the probability of success as the figure of merit, a relation between information causality and the non-local `inner-product game', and the derivation of a quadratic bound for these games. We then examine an entropic formulation of information causality with which one can obtain the same results, arguably in a simpler fashion.