  Quantum devices are subject to natural decay. We propose to study these decay
processes as the Markovian evolution of quantum channels, which leads us to
dynamical semigroups of superchannels. A superchannel is a linear map that maps
quantum channels to quantum channels, while satisfying suitable consistency
relations. If the input and output quantum channels act on the same space, then
we can consider dynamical semigroups of superchannels. No useful constructive
characterization of the generators of such semigroups is known. We characterize
these generators in two ways: First, we give an efficiently checkable criterion
for whether a given map generates a dynamical semigroup of superchannels.
Second, we identify a normal form for the generators of semigroups of quantum
superchannels, analogous to the GKLS form in the case of quantum channels. To
derive the normal form, we exploit the relation between superchannels and
semicausal completely positive maps, reducing the problem to finding a normal
form for the generators of semigroups of semicausal completely positive maps.
We derive a normal for these generators using a novel technique, which applies
also to infinite-dimensional systems. Our work paves the way to a thorough
investigation of semigroups of superchannels: Numerical studies become feasible
because admissible generators can now be explicitly generated and checked. And
analytic properties of the corresponding evolution equations are now accessible
via our normal form.
