Bounds for the divisibility-based and distinguishability-based   non-Markovianity measures
  We derive an upper bound for the distinguishability-based non-Markovianity measure of a two-level system and prove that for certain master equations the exact value of the measure achieves this bound. Furthermore, we obtain an easily calculable lower bound for the divisibility-based non-Markovianity measure of an $n$-level system. We illustrate the calculation of these bounds through examples, considering in detail the spin-boson model. We show that the differences between the two measures in the spin-boson model are caused by the drift vector that is also responsible for the non-unitality of the dynamical map. 
H. M\"akel\"a
quant-ph