  Spin filtering through quantum spin interference is addressed exactly, in two
dimensions, in a medium that has both Rashba and Dresselhaus spin-orbit
couplings and an applied external magnetic field. The problem is addressed from
the fully non-Abelian Gauge formulation. We propose an experimentally feasible
electronic Mach Zehnder Interferometer and solve for the perfect spin filtering
conditions. We find two broad solutions, one where filtering is achieved in the
original incoming basis, that is purely a non-Abelian solution, and the other
where one needs a tilted axis to observe the polarized output spinor. The
latter solution is well approximated by an Abelianized approximation. Both
solutions apply for arbitrary incoming polarization, and are only limited by
the randomness of the incoming spinor state.
