  A quantum two-path interferometer allows for direct measurement of the
transmission phase shift of an electron, providing useful information on
coherent scattering problems. In mesoscopic systems, however, the two-path
interference is easily smeared by contributions from other paths, and this
makes it difficult to observe the \textit{true} transmission phase shift. To
eliminate this problem, multi-terminal Aharonov-Bohm (AB) interferometers have
been used to derive the phase shift by assuming that the relative phase shift
of the electrons between the two paths is simply obtained when a smooth shift
of the AB oscillations is observed. Nevertheless the phase shifts using such a
criterion have sometimes been inconsistent with theory. On the other hand, we
have used an AB ring contacted to tunnel-coupled wires and acquired the phase
shift consistent with theory when the two output currents through the coupled
wires oscillate with well-defined anti-phase. Here, we investigate thoroughly
these two criteria used to ensure a reliable phase measurement, the anti-phase
relation of the two output currents and the smooth phase shift in the AB
oscillation. We confirm that the well-defined anti-phase relation ensures a
correct phase measurement with a quantum two-path interference. In contrast we
find that even in a situation where the anti-phase relation is less
well-defined, the smooth phase shift in the AB oscillation can still occur but
does not give the correct transmission phase due to contributions from multiple
paths. This indicates that the phase relation of the two output currents in our
interferometer gives a good criterion for the measurement of the \textit{true}
transmission phase while the smooth phase shift in the AB oscillation itself
does not.
