  A theoretical study of the polarization entanglement of two photons emitted
in the decay of metastable ionic states is performed within the framework of
density matrix theory and second-order perturbative approach. Particular
attention is paid to relativistic and non-dipole effects that become important
for medium- and high-$Z$ ions. To analyze these effects, the degree of
entanglement is evaluated both in the dipole approximation and within the
rigorous relativistic theory. Detailed calculations are performed for the
two-photon $2s_{1/2}\to 1s_{1/2}$ transition in hydrogen-like, as well as for
the $1s_{1/2}\, 2s_{1/2} \; {}^1S_0 \to 1s_{1/2}^2 \; {}^1S_0$, $1s_{1/2} \,
2s_{1/2} \; {}^3S_1\to 1s_{1/2}^2 \; {}^1S_0$ and $1s_{1/2} \, 2p_{1/2} \;
{}^3P_0\to 1s_{1/2}^2 \; {}^1S_0$ transitions in helium-like ions.
