Teleportation between distant qudits via scattering of mobile qubits

We consider a one-dimensional (1D) structure where non-interacting spin-$s$ scattering centers, such as quantum impurities or multi-level atoms, are embedded at given positions. We show that the injection into the structure of unpolarized flying qubits, such as electrons or photons, along with {path} detection suffice to accomplish spin-state teleportation between two centers via a third ancillary one. {No action over the internal quantum state of both the spin-$s$ particles and the flying qubits is required. The protocol enables the transfer of quantum information between well-seperated static entities in nanostructures by exploiting a very low-control mechanism, namely scattering.