A quantum channel is a completely positive trace-preserving linear transformation between matrix algebras. Complete positivity requires that tensoring the map with the identity map on an auxiliary matrix algebra preserves positive semidefinite matrices in every auxiliary dimension. Trace preservation ensures that density matrices map to density matrices.
In finite dimensions it has a Kraus representation 
with 
. Unitary conjugation is the special case with
a single unitary matrix 
. The no-disentanglers
conjecture concerns channels whose outputs approximate all separable states and
are always close to separable states.
