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Dimensionality-enhanced quantum state transfer in long-range interacting spin systems

In this work we study the single-qubit quantum state transfer in uniform long-range spin XXZ systems in high-dimensional geometries. We consider prototypical long-range spin exchanges that are relevant for experiments in cold atomic platforms: Coulomb, dipolar and van der Waals-like interactions. We find that in all these cases the fidelity increases with the dimensionality of the lattice. This can be related to the emergence of a pair of bilocalized states on the sender and receiver site due to the onset of an effective weak-coupling Hamiltonian. The enhancement of the quantum state transfer fidelity is more pronounced both with the increase of the couplings interaction range and in going from a 1D to a 2D lattice. Finally, we test our predictions in the presence of temperature-induced disorder introducing a model for the thermal displacement of the lattice sites, considered as a set of local adiabatic oscillators.