Subhankar Bera

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.