  Local Operations enhancing the entanglement of bipartite quantum states are
of great interest in quantum information processing. Subject of this paper are
local selective operations acting on single copies of states. Such operations
can lead to larger entanglement with respect to a certain measure as studies
before by the Horodeckis and A. Kent et al. (PRA 60,PRL 81 and 83). We present
a complete characterisation of all local operations yielding optimal
entanglement for pairs of qubits, extending former results of A. Kent et al. We
introduce a new technique for the classification of states according to their
behaviour under entanglement optimizing operations, using the entanglement
properties of the support of density matrices.
