  The electronic Hong-Ou-Mandel interferometer in the integer quantum Hall
regime is an ideal system to probe the building up of quantum correlations
between charge carriers and it has been proposed as a viable platform for
quantum computing gates. Using a parallel implementation of the split-step
Fourier method, we simulated the antibunching of two interacting fermionic wave
packets impinging on a quantum point contact. Numerical results of the exact
approach are compared with a simplified theoretical model based on
one-dimensional scattering formalism. We show that, for a realistic geometry,
the Coulomb repulsion dominates over the exchange energy, this effect being
strongly dependent on the energy broadening of the particles. We define
analytically the spatial entanglement between the two regions of the quantum
point contact, and obtain quantitatively its entanglement-generation
capabilities.
