  In order to cope with the fact that there exists no single maximally
entangled state (up to local unitaries) in the multipartite setting, we
introduced in [J. I. de Vicente, C. Spee and B. Kraus, Phys. Rev. Lett. 111,
110502 (2013)] the maximally entangled set of n-partite quantum states. This
set consists of the states that are most useful under conversion of pure states
via Local Operations assisted by Classical Communication (LOCC). We will review
our results here on the maximally entangled set of three- and generic
four-qubit states. Moreover, we will discuss the preparation of arbitrary (pure
or mixed) states via deterministic LOCC transformations. In particular, we will
consider the deterministic preparation of arbitrary three-qubit (four-qubit)
states via LOCC using as a resource a six-qubit (23-qubit) state respectively.
