  We study the fringe visibility and the distinguishability of a general
Mach-Zehnder interferometer with an asymmetric beam splitter. Both the fringe
visibility V and the distinguishability D are affected by the input state of
the particle characterized by the Bloch vector S=(Sx,Sy,Sz) and the second
asymmetric beam splitter characterized by paramter /beta. For the total system
is initially in a pure state, it is found that the fringe visibility reaches
the upper bound and the distinguishability reaches the lower bound when
cos(/beta) = -Sx. The fringe visibility obtain the maximum only if Sx = 0 and
/beta = /pi/2 when the input particle is initially in a mixed state. The
complementary relationship V2 + D2 <= 1 is proved in a general Mach-Zehnder
interferometer with an asymmetric beam splitter, and the conditions for the
equality are also presented.
