  The monogamy of nonlocality is one the most intriguing and cryptographically
significant predictions of quantum theory. The physical principle of
information causality offers a promising means to understand and restrict the
extent of nonlocality without invoking the abstract mathematical formalism of
quantum theory. In this article, we demonstrate that the original bipartite
formulation of information causality cannot imply non-trivial monogamy
relations, thereby refuting the previous claims. Nevertheless, we show that the
recently proposed multipartite formulation of information causality implies
stronger-than-no-signaling monogamy relations. We use these monogamy relations
to enhance the security of device-independent quantum key distribution against
a no-signaling eavesdropper constrained by information causality.
