  Quantum dynamical decoupling is a procedure to cancel the effective coupling
between two systems by applying sequences of fast actuations, under which the
coupling Hamiltonian averages out to leading order(s). One of its prominent
uses is to drive a target system in such a way as to decouple it from a less
protected one. The present manuscript investigates the dual strategy: acting on
a noisy "environment" subsystem such as to decouple it from a target system.
The potential advantages are that actions on the environment commute with
system operations, and that imprecisions in the decoupling actuation are
harmless to the target. We consider two versions of environment-side
decoupling: adding an imprecise Hamiltonian drive which stirs the environment
components; and, increasing the decoherence rates on the environment. The
latter can be viewed as driving the environment with pure noise and our
conclusions establish how, maybe counterintuitively, isolating the environment
from noise sources as much as possible is often not the best option. We
explicitly analyze the induced decoherence on the target system and establish
how it is influenced by the parameters in both cases. The analysis combines
Lindbladian derivation, adiabatic elimination, and Floquet modeling in a way
that may be of independent interest.
