Two-electron selective coupling in an edge-state based conditional phase shifter

We investigate the effect of long-range Coulomb interaction on the two-electron scattering in the integer quantum Hall regime at bulk filling factor two. We compute the dynamics of the exact two-particle wave function by means of a parallel version of the split-step Fourier method in a 2D potential background reproducing the effect of depleting gates in a realistic heterostructure, with the charge carrier represented by a localized wave packet of edge states. We compare the spatial shift induced by Coulomb repulsion in the final two-electron wave function for two indistinguishable electrons initialized in different configurations according to their Landau index and analyze their bunching probability and the effect of screening. We finally prove the feasibility of this device as a two-qubit conditional phase shifter able to generate controlled entanglement from product states.