Nonlocality of quantum states can be transitive

Abstract Despite the monogamous nature of nonlocal correlations, in a Bell test involving three parties A, B, and C, the nonlocality in two bipartite subsystems (e.g., AB and BC) may force the remaining bipartite subsystem (e.g., AC) to exhibit nonlocality. Although this intriguing effect of nonlocality transitivity has been identified in the non -quantum non-signaling world since 2011, whether such transitivity could manifest within quantum theory has remained unresolved. Here, we answer this open problem affirmatively—both analytically and numerically—at the level of quantum states, thereby showing that a quantum-realizable notion of nonlocality transitivity exists. In our analytic construction, we prove and use the fact that copies of the W -state marginals uniquely determine the global compatible state, thus establishing another instance when the parts determine the whole. Moreover, we present a simple method to construct quantum states and correlations that are nonlocal in all their non-unipartite marginals. We also discuss the implications of our results in (semi-) device-independent cryptographic and certification tasks.