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Capacities of quantum channels and decoherence times both quantify the extentto which quantum information can withstand degradation by interactions with itsenvironment. However, calculating capacities directly is known to beintractable in general. Much recent work has focused on upper bounding certaincapacities in terms of more tractable quantities such as specific norms fromoperator theory. In the meantime, there has also been substantial recentprogress on estimating decoherence times with techniques from analysis andgeometry, even though many hard questions remain open. In this article, weintroduce a class of continuous-time quantum channels that we calledtransferred channels, which are built through representation theory from aclassical Markov kernel defined on a compact group. We study two subclasses ofsuch kernels: H\"ormander systems on compact Lie-groups and Markov chains onfinite groups. Examples of transferred channels include the depolarizingchannel, the dephasing channel, and collective decoherence channels acting on$d$ qubits. Some of the estimates presented are new, such as those for channelsthat randomly swap subsystems. We then extend tools developed in earlier workby Gao, Junge and LaRacuente to transfer estimates of the classical Markovkernel to the transferred channels and study in this way differentnon-commutative functional inequalities. The main contribution of this articleis the application of this transference principle to the estimation of variouscapacities as well as estimation of entanglement breaking times, defined as thefirst time for which the channel becomes entanglement breaking. Moreover, ourestimates hold for non-ergodic channels such as the collective decoherencechannels, an important scenario that has been overlooked so far because of alack of techniques.

Group transference techniques for the estimation of the decoherence times and capacities of quantum Markov semigroups