Discussion of generalized monogamy relations for multipartite entanglement

The analytic convex roof expression for the entanglement of pairs of qubits marked a major breakthrough in the quantification of entanglement. An equally remarkable ''monogamy'' relation limits the way of distributing such pairwise qubit entanglement over a multi-qubit system and gave rise to the definition of a tri-partite entanglement measure. Already for this reason would it be desirable to have an extension of this monogamy relation in order to include multipartite entanglement beyond pairs. We discuss possible extensions of the monogamy relation for pairwise qubit entanglement. Based on recent advances for mixed state threetangle and known invariants for four qubits we systematically analyze pure states of four qubits. Though a class of states exists for which the monogamy relation can be extended in some form, we give a family of counterexamples where no monogamy equality does exist including the three- and/or some four-tangle