  Device-independent quantum key distribution (DIQKD) guarantees unconditional
security of secret key without making assumptions about the internal workings
of the devices used. It does so using the loophole-free violation of a Bell's
inequality. The primary challenge in realizing DIQKD in practice is the
detection loophole problem that is inherent to photonic tests of Bell's
inequalities over lossy channels. We revisit the proposal of Curty and Moroder
[Phys. Rev. A 84, 010304(R) (2011)] to use a linear optics-based
entanglement-swapping relay (ESR) to counter this problem. We consider
realistic models for the entanglement sources and photodetectors; more
precisely, (a) polarization-entangled states based on pulsed spontaneous
parametric downconversion (SPDC) sources with infinitely higher order
multi-photon components and multimode spectral structure, and (b) on-off
photodetectors with non-unit efficiencies and non-zero dark count
probabilities. We show that the ESR-based scheme is robust against the above
imperfections and enables positive key rates at distances much larger than what
is possible otherwise.
