Multi-terminal Aharonov-Bohm (AB) rings are ideal building blocks for quantum networks (QNs) thanks to their ability to map input states into controlled coherent superpositions of output states. We report on experiments performed on three-terminal Ga
As/Al_(x)Ga_(1-x)As AB devices and compare our results with a scattering-matrix model including Lorentz forces and decoherence. Our devices were studied as a function of external magnetic field (B) and gate voltage at temperatures down to 350 mK. The total output current from two terminals while applying a small bias to the third lead was found to be symmetric with respect to B with AB oscillations showing abrupt phase jumps between 0 and pi at different values of gate voltage and at low magnetic fields, reminiscent of the phase-rigidity constraint due to Onsager-Casimir relations. Individual outputs show quasi-linear dependence of the oscillation phase on the external electric field. We emphasize that a simple scattering-matrix approach can not model the observed behavior and propose an improved description that can fully describe the observed phenomena. Furthermore, we shall show that our model can be successfully exploited to determine the range of experimental parameters that guarantee a minimum oscillation visibility, given the geometry and coherence length of a QN.
