  The decoherence matrix studied by Gudder and Sorkin (2011) can be considered
as a map from the set of all the pairs of $n$-length paths to complex numbers,
which is induced by the discrete-time quantum walk. The decoherence matrix is
one of the decoherence functionals which present their historical quantum
measure theory. In this paper, we compute the von Neumann entropy of the
decoherence matrix. To do so, we use the result that the eigensystem of the
decoherence matrix can be expressed by a corresponding correlated random walk.
