  We derive an analytical description for the quantum state preparation using
systems of on-off detectors. Our method will apply the true click statistics of
such detector systems. In particular, we consider heralded quantum state
preparation using correlated light fields, photon addition and photon
subtraction processes. Using a post-selection procedure to a particular number
of clicks of the detector system, the output states reveal a variety of quantum
features. The rigorous description allows the identification and
characterization of fundamentally unavoidable attenuations within given
processes. We also generalize a known scenario of noiseless amplification with
click detectors for the purpose of the preparation of various types of
nonclassical states of light. Our exact results are useful for the choice of
experimental parameters to realize a target state.
