Semi-device-independent quantum key distribution based on a coherence equality.

We introduce a semi-device-independent quantum key distribution (SDI-QKD) protocol with trusted quantum inputs, and a classical Alice and Bob. The protocol is based on the Coherence Equality (CE) game recently introduced by del Santo and Daki\'c, which verifies a coherent quantum superposition of communication trajectories in a de-localized way. We show the protocol to be semi-device independent since the only trusted operations occur in the users' labs, and establish security against an adversary with bounded quantum memory. Finally, by merit of certifying entanglement in Fock space, we recast the setup of the protocol as a counterfactual test of nonlocality.