Multipartite pure-state entanglement

We show that pure states of multipartite quantum systems are multiseparable (i.e., give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the quantification of multipartite pure-state entanglement are discussed. Further, as an application of the techniques used here, we show that any purification of a bipartite-bound entangled state having a positive partial transpose is tri-inseparable, i.e., has none of its three bipartite partial traces separable.