  The entanglement production is key for many applications in the realm of
quantum information, but so is the identification of processes that allow to
create entanglement in a fast and sustained way. Most of the advances in this
direction have been circumscribed to bipartite systems only, and the rate of
entanglement in multipartite system has been much less explored.Here we
contribute to the identification of processes that favor the fastest and
sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type
states. By considering a three-party interaction Hamiltonian, we analyse the
dynamics of the 3-tangle and the entanglement rate to identify the optimal
local operations that supplement the Hamiltonian evolution in order to speed-up
the generation of three-way entanglement, and to prevent its decay below a
predetermined threshold value. The appropriate local operation that maximizes
the speed at which a highly-entangled state is reached has the advantage of
requiring access to only one of the qubits, yet depends on the actual state of
the system. Other universal (state-independent) local operations are found that
conform schemes to maintain a sufficiently high amount of 3-tangle. Our results
expand our understanding of entanglement rates to multipartite systems, and
offer guidance regarding the strategies that improve the efficiency in various
quantum information processing tasks.
