Interferometry with photons in a mixed state: how to calculate the fringe visibility?

Suppose that Bob and Alice receive from John photons described by this density matrix:
$begin{bmatrix}
0.5 & 0.5 cos(alpha)
0.5 cos(alpha) & 0.5
end{bmatrix} $

They use these photons as input of an interferometer. they get
a pattern with a given fringe visibility $V(alpha)$.
How to calculate it from the density matrix? Is it related to the entropy of the matrix?
does it help to rewrite it as mixture of two density matrices, one with maximal entropy and one pure density matrix?
if first has say a weight of 40 percent and the other 60
would i have the same if i begin with the H><H + V><V mixed state which gives no interference and follow by the 60 percent pure state which add interference? Does it help?