We investigate the relationship between non-Markovianity and the
effectiveness of a dynamical decoupling protocol for qubits undergoing pure
dephasing. We consider an exact model in which dephasing arises due to a
bosonic environment with a spectral density of the Ohmic class. This is
parametrised by an Ohmicity parameter by changing which we can model both
Markovian and non-Markovian environments. Interestingly, we find that
engineering a non-Markovian environment is detrimental to the efficiency of the
dynamical decoupling scheme, leading to a worse coherence preservation. We show
that each dynamical decoupling pulse reverses the flow of quantum information
and, on this basis, we investigate the connection between dynamical decoupling
efficiency and the reservoir spectral density. Finally, in the spirit of
reservoir engineering, we investigate the optimum system-reservoir parameters
for achieving maximum stationary coherences.Comment: 6 pages, 4 figure
