Can the exciton--polariton regime be defined by its quantum properties?

Using a simple fully quantum model in an effective exciton scheme that takes into account the system--environment interaction, we study the different regimes arising in a microcavity--quantum dot system. Our numerical calculations of the emission linewidth, emission energy, integrated intensity and second- and third-order correlation functions are in good qualitative agreement with reported experimental results. We show that the transition from the polariton-laser to the photon-laser regime can be defined through the critical points of both the negativity and the linear entropy of the steady state.