  The aim of this paper is to revisit the implications of complementarity when
we inject into a Mach Zehnder interferometer particles with internal structure,
prepared in special translational-internal entangled (TIE) states. This
correlation causes the path distinguishability to be phase dependent in
contrast to the standard case. We show that such a TIE state permits us to
detect small phase shifts along with almost perfect path distinguishability,
beyond the constraints imposed by complementarity on simultaneous which-way and
which-phase measurements for standard cases (when distinguishability is
independent of interferometric phase).
