  Recent observation that almost all quantum states bear non-classical
correlations [A. Ferraro et al, Phys. Rev. A 81, 052328 (2010)] may seem to
imply that the Markovian bipartite systems are practically deprived of zero
discord states. Nevertheless, complementary to the result of Ferraro et al, we
construct a model of a Markovian bipartite system providing zero discord for
arbitrary long time interval, that we term 'Markovian classicality'. Our model
represents a matter-of-principle formal proof, i.e. a sufficient condition for
the, otherwise not obvious, existence of Markovian classicality. Interestingly
enough, we are not able to offer any alternative to the model. Physical
relevance of the model is twofold. First, the model is in intimate relation to
the topics of quantum information locality, quantum discord saturation and
quantum decorrelation. Second, the model is of the general physical interest.
It pertains to a specific structure (decomposition into parts/subsystems) of a
composite system, not to a special physical kind of composite systems. Being a
characteristic of a structure, by definition, the model of Markovian
classicality is not a model of sudden death of discord. We emphasize wide-range
implications of our results.
