  Characterising the input-output photon-number distribution of an unknown
optical quantum channel is an important task for many applications in quantum
information processing. Ideally, this would require deterministic photon-number
sources and photon-number-resolving detectors, but these technologies are still
work-in-progress. In this work, we propose a general method to rigorously bound
the input-output photon number distribution of an unknown optical channel using
standard optical devices such as coherent light sources and
non-photon-number-resolving detectors/homodyne detectors. To demonstrate the
broad utility of our method, we consider the security analysis of practical
quantum key distribution systems based on calibrated single-photon detectors
and an experimental proposal to implement time-correlated single photon
counting technology using homodyne detectors instead of single-photon
detectors.
