Characterization of non-adaptive Clifford channels

Stabilizer circuits arise in almost every area of quantum computation and communication, so there is interest in studying them from an 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 realized 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.