  In the implementation of device-independent quantum key distribution we are
interested in maximizing the key rate, i.e. the number of key bits that can be
obtained per signal, for a fixed security parameter. In the finite size regime,
we furthermore also care about the minimum number of signals required before
key can be obtained at all. Here, we perform a fully finite size analysis of
device independent protocols using the CHSH inequality both for collective and
coherent attacks. For coherent attacks, we sharpen the results recently derived
in Arnon-Friedman et al., Nat. Commun. 9, 459 (2018), to reduce the minimum
number of signals before key can be obtained. In the regime of collective
attacks, where the devices are restricted to have no memory, we employ two
different techniques that exploit this restriction to further reduce the number
of signals. We then discuss experimental platforms in which DIQKD may be
implemented. We analyse Bell violations and expected QBER achieved in previous
Bell tests with distant setups and situate these parameters in the security
analysis. Moreover, focusing on one of the experimental platforms, namely
nitrogen-vacancy based systems, we describe experimental improvements that can
lead to a device-independent quantum key distribution implementation in the
near future.
