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We study the fringe visibility and the distinguishability of a generalMach-Zehnder interferometer with an asymmetric beam splitter. Both the fringevisibility V and the distinguishability D are affected by the input state ofthe particle characterized by the Bloch vector S=(Sx,Sy,Sz) and the secondasymmetric beam splitter characterized by paramter /beta. For the total systemis initially in a pure state, it is found that the fringe visibility reachesthe upper bound and the distinguishability reaches the lower bound whencos(/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. Thecomplementary relationship V2 + D2 <= 1 is proved in a general Mach-Zehnderinterferometer with an asymmetric beam splitter, and the conditions for theequality are also presented.

Fringe visibility and distinguishability in two-path interferometer with an asymmetric beam splitter