  Capacities of quantum channels and decoherence times both quantify the extent
to which quantum information can withstand degradation by interactions with its
environment. However, calculating capacities directly is known to be
intractable in general. Much recent work has focused on upper bounding certain
capacities in terms of more tractable quantities such as specific norms from
operator theory. In the meantime, there has also been substantial recent
progress on estimating decoherence times with techniques from analysis and
geometry, even though many hard questions remain open. In this article, we
introduce a class of continuous-time quantum channels that we called
transferred channels, which are built through representation theory from a
classical Markov kernel defined on a compact group. We study two subclasses of
such kernels: H\"ormander systems on compact Lie-groups and Markov chains on
finite groups. Examples of transferred channels include the depolarizing
channel, the dephasing channel, and collective decoherence channels acting on
$d$ qubits. Some of the estimates presented are new, such as those for channels
that randomly swap subsystems. We then extend tools developed in earlier work
by Gao, Junge and LaRacuente to transfer estimates of the classical Markov
kernel to the transferred channels and study in this way different
non-commutative functional inequalities. The main contribution of this article
is the application of this transference principle to the estimation of various
capacities as well as estimation of entanglement breaking times, defined as the
first time for which the channel becomes entanglement breaking. Moreover, our
estimates hold for non-ergodic channels such as the collective decoherence
channels, an important scenario that has been overlooked so far because of a
lack of techniques.
