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 a secret key without making assumptions about the internal workings of the devices used for distribution. 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 down-conversion sources with infinitely higher-order multiphoton components and multimode spectral structure, and (b) on-off photodetectors with nonunit efficiencies and nonzero 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.