Abstract The experimental setup for study of Compton scattering of entangled and decoherent annihilation gammas is described. These gammas are born in two-photon positron-electron annihilation. Polarizations of annihilation gammas are mutually orthogonal, while the polarization of each photon is indefinite. If one of the photons of the pair interacts with matter, the pair becomes decoherent and photons acquire the determined polarization states. The kinematics of Compton scattering depends on the polarization states and can be different for entangled and decoherent pairs of annihilation photons. The angular correlations of scattered gammas for both, entangled and decoherent states are measured and compared. It is shown, that the kinematics of Compton scattering are similar for both cases.