  Recently, a measure for the non-Markovian behavior of quantum processes in
open systems has been developed which is based on the quantification of the
flow of information between the open system and its environment [Phys. Rev.
Lett. 103, 210401 (2009)]. The information flow is connected to the rate of
change of the trace distance between quantum states which can be interpreted in
terms of the distinguishability of these states. Here, we elaborate the
mathematical details of this theory, present applications to specific physical
models, and discuss further theoretical and experimental implications, as well
as relations to alternative approaches proposed recently.
