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According to the entropy accumulation theorem, proving the unconditionalsecurity of a device-independent quantum key distribution protocol reduces toderiving tradeoff functions, i.e., bounds on the single-round von Neumannentropy of the raw key as a function of Bell linear functionals, conditioned onan eavesdropper's quantum side information. In this work, we describe how theconditional entropy can be bounded in the 2-input/2-output setting, where theanalysis can be reduced to qubit systems, by combining entropy bounds forvariants of the well-known BB84 protocol with quantum constraints on qubitoperators on the bipartite system shared by Alice and Bob. The approach givesanalytic bounds on the entropy, or semi-analytic ones in reasonable computationtime, which are typically close to optimal. We illustrate the approach on avariant of the device-independent CHSH QKD protocol where both bases are usedto generate the key as well as on a more refined analysis of the originalsingle-basis variant with respect to losses. We obtain in particular adetection efficiency threshold slightly below 80.26%, within reach of currentexperimental capabilities.

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