Certifying semi-device-independent security via wave-particle duality experiments

Wave-particle duality (WPD) is known to be equivalent to an entropic uncertainty relation (EUR) based on the min- and max-entropies, which have a clear operational meaning in quantum cryptography. Here, we derive a connection between wave-particle relations and the semi-device-independent (SDI) security framework. In particular, we express an SDI witness entirely in terms of two complementary interferometric quantities: visibility and input distinguishability. Applying a symmetry condition to the interferometric quantities, we identify a scenario in which the classical bound is violated and the security condition is met in wave-particle experiments with a tunable beam splitter (TBS). This enables the certification of non-classicality and the positivity of the key rate directly from complementary interferometric quantities, as well as from informational entropic quantities. Moreover, we perform a proof-of-principle experiment using orbital-angular-momentum (OAM) encoded quantum states of light in a tunable interferometer, validating our theoretical predictions. We analyze an improved bound on the SDI security condition for qubits, effectively enlarging the parameter region where secure communication can be certified. Finally, we extend the framework to multipath interferometers, establishing that the fundamental correspondence between information-access limitations and interferometric complementarity, demonstrated in the two-path scenario, persists across arbitrary dimensions.