  Stabilizer circuits arise in almost every area of quantum computation and
communication, so there is an interest in studying them from
information-theoretic perspective, i.e. as quantum channels. We consider
several natural approaches to what can be called a Clifford channel: the
channel that can be realised by a stabilizer circuit without classical control,
the channel that sends pure stabilizer states to mixed stabilizer states, the
channel with stabilizer Choi state, the channel whose Stinespring dilation can
have a Clifford unitary. We show the equivalence of these definitions. Up to
unitary encoding and decoding maps any Clifford channel is a product of
stabilizer state preparations, qubit discardings, identity channels and full
dephasing channels. This simple structure allows to compute information
capacities of such channels.
