  We study the non-Markovianity of the dynamics of open quantum systems
focusing on the cases of independent and common environmental interactions. We
investigate the degree of non-Markovianity quantified by two distinct measures
proposed by Luo, Fu and Song (LFS) and Breuer, Laine and Pillo (BLP). We show
that the amount of non-Markovianity, for a single and a pair of qubits, depends
on the quantum process, the proposed measure and whether the environmental
interaction is collective or independent. In particular, we demonstrate that
while the degree of non-Markovianity generally increases with the number of the
qubits in the system for independent environments, the same behavior is not
always observed for common environments. In the latter case, our analysis
suggests that the amount of non-Markovianity could increase or decrease
depending on the properties of the considered quantum process.
