We investigate the dynamical properties of the
two-boson quantum walk in systems with different degrees
of coherence, and where the effect of the coherence
on the two-boson quantum walk can be naturally introduced.
A general analytical expression for the two-boson
correlation function, for both pure states and mixed states,
is given.We propose a possible two-photon quantum-walk
scheme with a mixed initial state, and find that the twophoton
correlation function and the average distance between
two photons can be influenced by the initial photon
distribution, the relative phase, or the degree of coherence.
The propagation features of our numerical results can be
explained by our analytical two-photon correlation function.