Michele Masini

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.

Quantum Key Distribution (QKD) enables provable secure communication but faces challenges in device characterization, posing potential security risks. Device-Independent (DI) QKD protocols overcome this issue by making minimal device assumptions but are limited in distance because they require high detection efficiencies, which refer to the ability of the experimental setup to detect quantum states. Our study explores an entanglement-based one-sided device-independent QKD scenario, where one party's device is semi-trusted, while the second is completely untrusted. We introduce specific assumptions about the semi-trusted device's measurements and assess the security of our protocol without post-selecting outcomes, thereby allowing one to prove security against coherent attacks. By applying the latest analytical and numerical methods, we established that our protocol can securely operate as long as the involved detection efficiencies exceed a minimal threshold of 50.1% specifically on the untrusted side. This is almost the theoretical limit achievable for protocols with two untrusted measurements and is within current experimental capabilities. Interestingly, we also show that, by placing the source of states close to the untrusted side, our protocol is secure over distances comparable to standard QKD protocols. Our findings not only reinforce the practicality of QKD systems under less stringent conditions but also serve as a feasible hybrid approach, bridging conventional QKD with DI QKD.