  Several realistic spin-orbital models for transition metal oxides go beyond
the classical expectations and could be understood only by employing the
quantum entanglement. Experiments on these materials confirm that spin-orbital
entanglement has measurable consequences. Here, we capture the essential
features of spin-orbital entanglement in complex quantum matter utilizing 1D
spin-orbital model which accommodates SU(2)xSU(2) symmetric Kugel-Khomskii
superexchange as well as the Ising on-site spin-orbit coupling. Building on the
results obtained for full and effective models in the regime of strong
spin-orbit coupling, we address the question whether the entanglement found on
superexchange bonds always increases when the Ising spin-orbit coupling is
added. We show that (i) quantum entanglement is amplified by strong spin-orbit
coupling and, surprisingly, (ii) almost classical disentangled states are
possible. We complete the latter case by analyzing how the entanglement
existing for intermediate values of spin-orbit coupling can disappear for
higher values of this coupling.
