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. We also find a pronounced enhancement of the fidelity in one-dimensional lattices for increasing interaction range. 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. 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.

• Received 18 December 2019
• Revised 8 April 2020
• Accepted 13 April 2020

DOI:https://doi.org/10.1103/PhysRevA.101.053607