  Single-qubit channels are studied under two broad classes: amplitude damping
channels and generalized depolarizing channels. A canonical derivation of the
Kraus representation of the former, via the Choi isomorphism is presented for
the general case of a system's interaction with a squeezed thermal bath. This
isomorphism is also used to characterize the difference in the geometry and
rank of these channel classes. Under the isomorphism, the degree of decoherence
is quantified according to the mixedness or separability of the Choi matrix.
Whereas the latter channels form a 3-simplex, the former channels do not form a
convex set as seen from an ab initio perspective. Further, where the rank of
generalized depolarizing channels can be any positive integer upto 4, that of
amplitude damping ones is either 2 or 4. Various channel performance parameters
are used to bring out the different influences of temperature and squeezing in
dissipative channels. In particular, a noise range is identified where the
distinguishability of states improves inspite of increasing decoherence due to
environmental squeezing.
