  The postselection technique is an important proof technique for proving the
security of quantum key distribution protocols against coherent attacks. In
this work, we go through multiple steps to rigorously apply the postselection
technique to optical quantum key distribution protocols. First, we place the
postselection technique on a rigorous mathematical foundation by fixing a
technical flaw in the original postselection paper. Second, we extend the
applicability of the postselection technique to prepare-and-measure protocols
by using a de Finetti reduction with a fixed marginal. Third, we show how the
postselection technique can be used for decoy-state protocols by tagging the
source. Finally, we extend the applicability of the postselection technique to
realistic optical setups by developing a new variant of the flag-state
squasher. We also improve existing de Finetti reductions, which reduce the
effect of using the postselection technique on the key rate. These improvements
can be more generally applied to other quantum information processing tasks. As
an example to demonstrate the applicability of our work, we apply our results
to the time-bin encoded three-state protocol. We observe that the postselection
technique performs better than all other known proof techniques against
coherent attacks.
