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The estimation of high order correlation function values is an importantproblem in the field of quantum computation. We show that the problem can bereduced to preparation and measurement of optical quantum states resultingafter annihilation of a set number of quanta from the original beam. We applythis approach to explore various photon bunching regimes in optical states withgamma-compounded Poisson photon number statistics. We prepare and performmeasurement of the thermal quantum state as well as states produced bysubtracting one to ten photons from it. Maximum likelihood estimation isemployed for parameter estimation. The goal of this research is the developmentof highly accurate procedures for generation and quality control of opticalquantum states.

Study of higher-order correlation functions and photon statistics using multiphoton-subtracted states and quadrature measurements