Information causality beyond the random access code model

TL;DR

This paper introduces a new quantifier for information causality that helps better distinguish quantum correlations from non-quantum ones, closing some existing gaps in the boundary characterization.

Contribution

It proposes a novel measure based on redundant information, removing reliance on random access code success criteria, and provides numerical evidence of its effectiveness.

Findings

New quantifier aligns with quantum correlations

Closes gaps in quantum boundary characterization

Numerical evidence supports the new measure

Abstract

Information causality (IC) was one of the first principles that have been invoked to bound the set of quantum correlations. For some families of correlations, this principle recovers exactly the boundary of the quantum set; for others, there is still a gap. We close some of these gaps using a new quantifier for IC, based on the notion of ``redundant information''. This progress was made possible by the recognition that the principle of IC can be captured without referring to the success criterion of random access codes. We give strong numerical evidence that the new definition is still obeyed by quantum correlations in the same scenario.