  We generalize Grover algorithm with two arbitrary phases in a density matrix
set up. We give exact analytic expressions for the success probability after
arbitrary number of iteration of the generalized Grover operator as a function
of number of iterations, two phase angles ({\alpha}, \{beta}) and parameter
{\xi} introduced in the off diagonal terms of the density matrix in a sense to
capture the coherence present in the initial quantum register. We extend Li and
Li's idea and show for the phase matching condition {\alpha} = -\{beta} =
0.35{\pi} with two iterations and {\xi} = 1, we can achieve success probability
>= 0.8 only with a knowledge about the lower bound of {\lambda} = 0.166 where
{\lambda} is the ratio of marked to total number states in the database.
Finally we quantify success probability of the algorithm with decrease in
coherence of the initial quantum state against modest noise in this simple
model.
