  We construct relativistic quantum Markov semigroups from covariant completely
positive maps. We proceed by generalizing a step in Stinespring's dilation to a
general system of imprimitivity and basing it on Poincar\'e group. The
resulting noise channels are relativistically consistent and the method is
applicable to any fundamental particle, though we demonstrate it for the case
of light-like particles. The Krauss decomposition of the relativistically
consistent completely positive identity preserving maps (our set up is in
Heisenberg picture) enables us to construct the covariant quantum Markov
semigroups that are uniformly continuous. We induce representations from the
little groups to ensure the quantum Markov semigroups that are ergodic due to
transitive systems imprimitivity.
