Information Causality as a Tool for Bounding the Set of Quantum Correlations

Area of Science:

• Quantum Information Theory
• Foundations of Quantum Mechanics
• Bell Nonlocality

Background:

• Information causality, a physical principle, was introduced to derive quantum mechanics predictions for Bell experiment correlations.
• It previously implied the Uffink inequality, approximating quantum correlations and Tsirelson's bound for the CHSH inequality.
• Generalizing information causality's implications for nonlocal correlations proved challenging.

Purpose of the Study:

• To present a novel technique for deriving polynomial inequalities from information causality in bipartite Bell scenarios.
• To establish information causality as an efficient tool for approximating the set of quantum correlations.
• To explore improved statements of information causality and derive tighter constraints.

Main Methods:

• Developing a simple technique to generate polynomial inequalities from information causality.
• Applying the technique to bipartite Bell scenarios with binary outcomes and equal measurement settings.
• Proposing an enhanced information causality principle and deriving new inequalities.

Main Results:

• A family of inequalities is derived, non-trivially constraining nonlocal correlations in specific Bell scenarios.
• The method demonstrates information causality's efficacy in approximating quantum correlation sets.
• A tighter constraint beyond the Uffink inequality is obtained for the simplest Bell scenario.

Conclusions:

• The presented technique simplifies the application of information causality to bound physical correlations.
• Information causality is now a more versatile tool for studying quantum and nonlocal correlations.
• The findings offer a refined understanding of the boundary of the quantum set in Bell scenarios.