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Information causality was initially proposed as a physical principle aimed atderiving the predictions of quantum mechanics on the type of correlationsobserved in the Bell experiment. In the same work, information causality wasfamously shown to imply the Uffink inequality that approximates the set ofquantum correlations and rederives Tsirelson's bound of theClauser-Horne-Shimony-Holt inequality. This result found limitedgeneralizations due to the difficulty of deducing implications of theinformation causality principle on the set of nonlocal correlations. In thispaper, we present a simple technique for obtaining polynomial inequalities frominformation causality, bounding the set of physical correlations in any Bellscenario. To demonstrate our method, we derive a family of inequalities whichnon-trivially constrains the set of nonlocal correlations in Bell scenarioswith binary outcomes and equal number of measurement settings. Finally, wepropose an improved statement of the information causality principle, obtaintighter constraints for the simplest Bell scenario that goes beyond the Uffinkinequality, and recovers a part of the boundary of the quantum set.

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