  We categorize quantum gates according to their capability to generate genuine
multipartite entanglement based on the hierarchy of multipartite separable
states. In particular, when a fixed unitary operator acts on the set of
k-separable states, the maximal (average) genuine multipartite entanglement
(GME) content produced via that particular unitary operator is determined after
maximizing over the set of k-separable input states. We identify unitary
operators that are beneficial for generating high GME when the input states are
entangled in some bipartition, although the picture can also be reversed in
which entanglement in inputs does not help. We characterize maximum entangling
power of a variety of unitary operators including special classes of quantum
gates, diagonal, permutation and Haar uniformly generated unitary operators by
computing generalized geometric measure (GGM) as GME quantifier. We determine
the unitary operators and their corresponding inputs which can create the
resulting states having maximum GGM.
