Maria Balanzó-Juandó

Bridging the gap between practical implementation and rigorous security, semi-device-independent quantum key distribution (QKD) offers a compelling middle ground—requiring minimal trust assumptions while achieving key rates competitive with fully characterized protocols. We investigate two conceptually distinct constraints on the preparation device: the information constraint and restricted distrust. We identify protocols that remain secure under both assumptions and demonstrate their robustness to experimental noise. Notably, the widely used BB84 and B92 protocols fail to provide security under the information constraint. To obtain secure key rates, we showcase a numerical framework combining tracial non-commutative polynomial optimization with entropy relaxation techniques. Our approach extends naturally to broader classes of preparation constraints and QKD protocols.

Device-independent quantum key distribution is a secure quantum cryptographic paradigm that allows two honest users to establish a secret key, while putting minimal trust in their devices. Most of the existing protocols have the following structure: First, a bipartite nonlocal quantum state is distributed between the honest users, who perform local projective measurements to establish nonlocal correlations. Then, they announce the implemented measurements and extract a secure key by post-processing their measurement outcomes. We show that no protocol of this form allows for establishing a secret key when implemented on certain entangled nonlocal states, namely on a range of entangled two-qubit Werner states. To prove this result, we introduce a technique for upper-bounding the asymptotic key rate of device-independent quantum key distribution protocols, based on a simple eavesdropping attack. Our results imply that either different tools---such as different reconciliation techniques or non-projective measurements---are needed for device-independent quantum key distribution in the large-noise regime, or Bell nonlocality is not sufficient for this task.