Progress towards practical device-independent quantum key distribution with spontaneous parametric down-conversion sources, on-off photodetectors, and entanglement swapping

Device-independent quantum key distribution (DIQKD) guarantees unconditional security of secret key without making assumptions about the internal workings of the devices used. 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. Our results show that the imperfect ESR-based scheme still enables positive key rates at distances much larger than what is possible without ESR for sufficiently large detector and coupling efficiencies, small dark count probabilities in the detectors and small spectral spread in the sources.