Information causality as a tool for bounding the set of quantum correlations

TL;DR

This paper introduces a simple polynomial inequality technique based on information causality to better approximate and bound the set of quantum correlations in bipartite Bell scenarios, improving previous constraints.

Contribution

The authors develop a straightforward method to derive polynomial inequalities from information causality, enhancing the ability to bound quantum correlations in bipartite Bell scenarios.

Findings

Derived a family of inequalities constraining nonlocal correlations.

Proposed an improved statement of information causality.

Recovered part of the quantum set boundary beyond previous inequalities.

Abstract

Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in the Bell experiment. In the same work, information causality was famously shown to imply the Uffink inequality that approximates the set of quantum correlations and rederives Tsirelson's bound of the Clauser-Horne-Shimony-Holt inequality. This result found limited generalizations due to the difficulty of deducing implications of the information causality principle on the set of nonlocal correlations. In this paper, we present a simple technique for obtaining polynomial inequalities from information causality bounding the set of physical correlations in any bipartite Bell scenario. This result makes information causality an efficient tool for approximating the set of quantum correlations. To demonstrate our method, we derive a family of inequalities which non-trivially constrains the set of nonlocal correlations in Bell scenarios with binary outcomes and equal number of measurement settings. Finally, we propose an improved statement of the information causality principle and obtain a tighter constraint for the simplest Bell scenario, that goes beyond the Uffink inequality and recovers a part of the boundary of the quantum set.