Quantum beats of light polarization and condition of complete positivity

An open spin system with spin $J=1$ interacting with an axisymmetric environment is considered. It is shown that if the symmetry group of the environment is $SO(2)$ or $SO(2)\times\mathbb Z_2^c$ then quantum beats of the polarization of the radiated light are possible. If the symmetry group of the environment is one of the groups $O(2)$, $O(2)^-$, $O(2)\times\mathbb Z_2^c$ then quantum polarization beats are not realized.