Yeong-Cherng Liang

As a striking manifestation of quantum entanglement, nonlocality has long played a pivotal role in shaping our understanding of the quantum world. When considering a Bell test involving three parties, we may even find a remarkable situation where the nonlocality in two bipartite subsystems forces the remaining bipartite subsystem to exhibit nonlocality. This intriguing effect, dubbed nonlocality transitivity, was first identified in the non-quantum non-signaling world in 2011. However, whether such transitivity could manifest within quantum theory has remained unresolved—until now. Here, we provide the first affirmative answer to this open problem at the level of quantum states, thereby showing that there exists a quantum-realizable notion of nonlocality transitivity. Specifically, by leveraging the possibility of Bell-inequality violation by tensoring, we analytically construct a pair of nonlocal bipartite states such that simultaneously realizing them in a tripartite system induces nonlocality in the remaining bipartite subsystem. En route to showing this, we also prove that multiple copies of the W-state marginals uniquely determine the global compatible state, thus establishing another instance when the parts determine the whole. Surprisingly, the nonlocality transitivity of quantum states also occurs among the reduced states of Haar-random three-qutrit pure states. We further show that the transitivity of quantum steering can already be demonstrated with the marginals of a three-qubit W state, showing again another noteworthy difference between the two forms of quantum correlations. Finally, we present a simple method to construct quantum states and correlations that are nonlocal in all their non-unipartite marginals, which may be of independent interest.

Conference key agreement allows multiple parties to establish a shared secret key. Device-independent protocols are especially attractive because their security can be certified from observed correlations, without trusting the internal behavior of the devices. We propose a tripartite device-independent conference key agreement protocol using only two measurement bases on a shared GHZ state. Under suitable structural conditions, the maximal violation of a chosen Bell inequality self-tests the target GHZ strategy with Pauli measurements, ensuring ideal security. We also prove robust self-testing, showing that near-maximal violation guarantees nontrivial fidelity with the ideal strategy under realistic noise.

Device-independent quantum key distribution allows two distant parties to certify a secret key directly from the correlations observed in an experiment, without relying on a detailed model of the devices. In this work, we study this task in the minimal Bell scenario, where each party has only two measurement choices and two possible outcomes. We show that secure key generation can be certified in this simplest setting by using tailored Bell inequalities together with simple constraints on the observed probabilities. In particular, we identify a family of quantum correlations that enables perfect key generation in a spot-checking protocol. The security follows from a self-testing property: the observed data certify the relevant quantum state and measurements, and hence certify that the adversary has no information about the generated key. Our results show that maximal device-independent key generation is possible in the minimal Bell scenario, even for arbitrarily small Bell non-locality. This highlights the importance of using the full structure of the observed correlations, rather than only a single Bell-inequality value, for certifying device-independent quantum key distribution.