Entanglement witnesses provide a standard tool for the analysis of
entanglement in experiments. We investigate possible nonlinear entanglement
witnesses from several perspectives. First, we demonstrate that they can be
used to show that the set of separable states has no facets. Second, we give a
new derivation of nonlinear witnesses based on covariance matrices. Finally, we
investigate extensions to the multipartite case.Comment: 12 pages, 2 figures, for the proceedings of DICE2006 in Piombino
(Italy
