  Besides being a beautiful idea, device-independent quantum key distribution
(DIQKD) is probably the ultimate solution to defeat quantum hacking. To
guarantee security, it requires, however, that the fair-sampling loophole is
closed, which results in a very limited maximum achievable distance. To
overcome this limitation, DIQKD must be furnished with fair-sampling devices
like, for instance, qubit amplifiers. These devices can herald the arrival of a
photon to the receiver and thus decouple channel loss from the selection of the
measurement settings. Consequently, one can safely postselect the heralded
events and discard the rest, which results in a significant enhancement of the
achievable distance. In this work, we investigate photonic-based DIQKD assisted
by two main types of qubit amplifiers in the finite data block size scenario,
and study the resources -- particularly, the detection efficiency of the
photodetectors and the quality of the entanglement sources -- that would be
necessary to achieve long-distance DIQKD within a reasonable time frame of
signal transmission.
