  Quantum non-Markovianity of channels can be produced by mixing Markovian
channels, as observed recently by various authors. We consider an analogous
question of whether singularities of the channel can be produced by mixing
non-singular channels, i.e., ones that lack them. Here we answer the question
in the negative in the context of qubit Pauli channels. On the other hand,
mixing channels with a singularity can lead to the elimination of singularities
in the resultant channel. We distinguish between two types of singular
channels, which lead under mixing to broadly quite different properties of the
singularity in the resultant channel. The connection to non-Markovianity (in
the sense of completely positive indivisibility) is pointed out. These results
impose nontrivial restrictions on the experimental realization of
non-invertible quantum channels by a process of channel mixing.
