On measures of non-Markovianity: divisibility vs. backflow of   information
  We analyze two recently proposed measures of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a toy model to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures. 
Dariusz Chru\'sci\'nski, Andrzej Kossakowski, \'Angel Rivas
quant-ph math-ph math.MP