  The ability to reach a maximally entangled state from a separable one through
the use of a two-qubit unitary operator is analyzed for mixed states. This
extension from the known case of pure states shows that there are at least two
families of gates which are able to give maximum entangling power for all
values of purity. It is notable that one of this gates coincides with a maximum
discording one. We give analytical proof that such gate is indeed perfect
entangler at all purities and give numerical evidence for the existence of the
second one. Further, we find that there are other gates, many in fact, which
are perfect entanglers for a restricted range of purities. This highlights the
fact that many perfect entangler gates could in principle be found if a
thorough analysis of the full parameter space is performed.
