  We determine the shared information that can be extracted from time-bin
entangled photons using frame encoding. We consider photons generated by a
general down-conversion source and also model losses, dark counts and the
effects of multiple photons within each frame. Furthermore, we describe a
procedure for including other imperfections such as after-pulsing, detector
dead-times and jitter. The results are illustrated by deriving analytic
expressions for the maximum information that can be extracted from
high-dimensional time-bin entangled photons generated by a spontaneous
parametric down conversion. A key finding is that under realistic conditions
and using standard SPAD detectors one can still choose frame size so as to
extract over 10 bits per photon. These results are thus useful for experiments
on high-dimensional quantum-key distribution system.
