Reduced quantum dynamics with initial system-environment correlations characterized by pure Markov states

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 is a pure Markov state if and only if the bipartite marginal state of the 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 the 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 states are analyzed and it has been shown that all these correlations are entirely specified by the entropy of environment. Some implications concerning perfect quantum error correction procedure and quantum Markovian dynamics are presented.