  Polarization properties of the photons emitted in the two-photon decay of
hydrogen-like ions are studied within the framework of the density matrix and
second-order perturbation theory. In particular, we derive the polarization
correlation function that gives the probability of the (two-photon) coincidence
measurement performed by polarization-sensitive detectors. Detailed
calculations of this function are performed for the $2s_{1/2} \to 1s_{1/2}$
transition in neutral hydrogen as well as Xe$^{53+}$ and U$^{91+}$ ions. The
obtained results allow us to understand the influence of relativistic and
non-dipole effects on the polarization correlations in the bound-bound
two-photon transitions in heavy ions.
