Robustness of tripartite entanglement transfer from bosonic modes to localized qubits

We address entanglement transfer from a three-mode bosonic system to a tripartite systems of spatially separated flying or fixed qubits through the interaction with their local environments. We focus on the robustness of entanglement transfer against several effects, including off-resonant interactions for both qubit-local environment and local environment-bosonic mode subsystems, and also exploring the effect of changing the coupling constants, with the possibility to have different values for each qubit-local environment interaction. For the entangled bosonic modes we consider both Gaussian states and qubit-like states, comparing three different Generalized Schmidt Decompositions forms widely used in the literature and analyzing how the deviation from qubit-like approximation influences entanglement transfer. Finally, we investigate the multimode coupling between bosonic modes and each local environment showing a comparison between various qubit-like initial states and discussing how to improve the efficiency of entanglement transfer.