Entanglement generation by qubit scattering in three dimensions

A qubit (a spin-1/2 particle) prepared in the up state is scattered by local spin-flipping potentials produced by the two target qubits (two fixed spins), both prepared in the down state, to generate an entangled state in the latter when the former is found in the down state after scattering. The scattering process is analyzed in three dimensions, both to lowest order and in full order in perturbation, with an appropriate renormalization for the latter. The entanglement is evaluated in terms of the concurrence as a function of the incident and scattering angles, the size of the incident wave packet, and the detector resolution to clarify the key elements for obtaining an entanglement with high quality. The characteristics of the results are also discussed in the context of (in)distinguishability of alternative paths for a quantum particle.