  We investigate unitary operators acting on a tensor product space, with the
property that the quantum channels they generate, via the Stinespring dilation
theorem, are of a particular type, independently of the state of the ancilla
system in the Stinespring relation. The types of quantum channels we consider
are those of interest in quantum information theory: unitary conjugations,
constant channels, unital channels, mixed unitary channels, PPT channels, and
entanglement breaking channels. For some of the classes of bipartite unitary
operators corresponding to the above types of channels, we provide explicit
characterizations, necessary and/or sufficient conditions for membership, and
we compute the dimension of the corresponding algebraic variety. Inclusions
between these classes are considered, and we show that for small dimensions,
many of these sets are identical.
