Security of device-independent quantum key distribution via monogamy relations from multipartite information causality

The information causality principle (ℐ𝒞) was originally proposed as a promising means to understand the extent of quantum nonlocality without invoking the full mathematical formalism of quantum theory. Beyond the foundational significance, the problem of bounding nonlocal correlations by reasonable physical principles has meaningful practical consequences, particularly for device-independent (DI) cryptographic security. In this work, we advance in this direction, demonstrating that the ℐ𝒞 is enough to ensure DI security on quantum key distribution (QKD) protocols. Security is proven for a range of theoretically quantum-attainable parameters against individual attacks by a potentially postquantum eavesdropper. This result follows as a consequence of a strong form of monogamy of Bell's inequality violations, which we prove to be implied by the recently proposed multipartite formulation for ℐ𝒞. Additionally, we demonstrate that the original bipartite formulation of ℐ𝒞 fails to imply monogamy relations, and hence, ensure security of DIQKD, thus stressing the necessity of the multipartite framework.