Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints

According to the entropy accumulation theorem, proving unconditional security of a device-independent quantum key distribution protocol reduces deriving tradeoff functions, i.e., bounds on single-round von Neumann raw as function Bell linear functionals, conditioned an eavesdropper's side information. In this work, we describe how conditional can be bounded in 2-input/2-output setting, where analysis reduced qubit systems, by combining for variants well-known BB84 with constraints operators bipartite system shared Alice and Bob. The approach gives analytic entropy, or semi-analytic ones reasonable computation time, which are typically close optimal. We illustrate variant CHSH QKD both bases used generate well more refined original single-basis respect losses. obtain particular detection efficiency threshold slightly below 80.26%, within reach current experimental capabilities.