We study both the wave-like behavior and particle-like behavior in a general Mach-Zehnder interferometer with its asymmetric beam splitter. A error-free measurement in the detector is used to extract the which-path information. The fringe visibility V and the which-path information I path are derived: their complementary relation V + I path ≤ 1 are found, and the condition for the equality is also presented.

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 vectorand the second asymmetric beam splitter characterized by paramter β. 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 β = −S x . The fringe visibility obtain the maximum only if S x = 0 and β = π/2 when the input particle is initially in a mixed state. The complementary relationship V 2 + D 2 ≤ 1 is proved in a general Mach-Zehnder interferometer with an asymmetric beam splitter, and the conditions for the equality are also presented.

We study both the two-particle and single-particle fringe visibility in the generalized version of the Nakazato–Pascazio model where two qubits interact with a finite length one-dimensional array. Both the two-particle and single-particle fringe visibilities are investigated with different initial states of the particles spin. For different initial states of the particles spin, the two-particle fringe visibility either decreases or increases over time, and may even decrease first and increase later. Due to the interaction between the particles and the one-dimensional array, the single-particle fringe visibility increases over time when the initial state of the two particles spin is independent. The single-particle fringe visibility is equal to 0 as the two-particle spin is initially in the completely entangled state or in the singlet state.