Quantum state engineering by click counting

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.