  The work by Christandl, K\"onig and Renner [Phys. Rev. Lett. 102, 020504
(2009)] provides in particular the possibility of studying unconditional
security in the finite-key regime for all discrete-variable protocols. We spell
out this bound from their general formalism. Then we apply it to the study of a
recently proposed protocol [Laing et al., Phys. Rev. A 82, 012304 (2010)]. This
protocol is meaningful when the alignment of Alice's and Bob's reference frames
is not monitored and may vary with time. In this scenario, the notion of
asymptotic key rate has hardly any operational meaning, because if one waits
too long time, the average correlations are smeared out and no security can be
inferred. Therefore, finite-key analysis is necessary to find the maximal
achievable secret key rate and the corresponding optimal number of signals.
