  Few studies explored the dynamics of non-classical correlations besides
entanglement in open multipartite quantum systems. Here, we address the
time-evolution of quantum discord and entanglement in a model of three
non-interacting qubits subject to a classical random telegraph noise in common
and separated environments. Two initial entangled states of the system are
examined, namely the GHZ- and W-type states. The dynamics of quantum
correlations results to be strongly affected by the input configuration of the
qubits, the type of the system-environment interaction, and the memory
properties of the environmental noise. When the qubits are non-locally coupled
to the random telegraph noise, the GHZ-type states partially preserve, at long
times, both discord and entanglement, regardless the correlation time of the
environmental noise. The survived entangled states turn out to be also
detectable by means of suitable entanglement witnesses. On the other hand, in
the same conditions, the decohering effects suppress all the quantum
correlation of the W-type states which are thus less robust than the GHZ-type
ones. The long-time survival of tripartite discord and entanglement opens
interesting perspectives in the use of multipartite entangled states for
practical applications in quantum information science.
