  In this paper we study diagonal quantum channels and their structure by
proving some results and giving most applicable instances of them. Firstly, it
is shown that action of every diagonal quantum channel on pure state from
computational basis is a convex combination of pure states determined by some
transition probabilities. Finally, by using the Cholesky decomposition it is
presented an algorithmic method to find an explicit form for Kraus operators of
diagonal quantum channels.
