  We generalize a recent result stating that all analytic quantum dynamics can
be represented exactly as the reduction of unitary dynamics generated by a
time-dependent Hamiltonian. More precisely, we prove that the partial trace
over analytic paths of unitaries can approximate any Lipschitz-continuous
quantum dynamics arbitrarily well. Equivalently, all such dynamics can be
approximated by analytic Kraus operators. We conclude by discussing potential
improvements and generalizations of these results, their limitations, and the
general challenges one has to overcome when trying to relate dynamics to
quantities on the system-environment level.
