  Any tripartite state which saturates the strong subadditivity relation for
the quantum entropy is defined as the Markov state.A tripartite pure state
describing an open system, its environment and their purifying system isa pure
Markov state iff the bipartite marginal state of purifying system and
environment is a product state. It has been shown that as long as the
purification of the input system-environment state is a pure Markov state the
reduced dynamics of the open system can be described, on the support of initial
system state, by a quantum channel for every joint unitary evolution of the
system-environment composite even in the presence of initial correlations.
Entanglement, discord and classical correlations of the initial
system-environment states implied by the pure Markov state are analyzed and it
has been shown that all these correlations are entirely specified by the
entropy of the environment. Some implications concerning perfect quantum error
correction procedure and quantum Markovian dynamics are presented.
