  The estimation of high order correlation function values is an important
problem in the field of quantum computation. We show that the problem can be
reduced to preparation and measurement of optical quantum states resulting
after annihilation of a set number of quanta from the original beam. We apply
this approach to explore various photon bunching regimes in optical states with
gamma-compounded Poisson photon number statistics. We prepare and perform
measurement of the thermal quantum state as well as states produced by
subtracting one to ten photons from it. Maximum likelihood estimation is
employed for parameter estimation. The goal of this research is the development
of highly accurate procedures for generation and quality control of optical
quantum states.
