N-Qubit W States are Determined by their Bipartite Marginals

We prove that the most general W class of N-qubit states are uniquely determined among arbitrary states (pure or mixed) by just their bipartite reduced density matrices. Moreover, if we consider only pure states, then (N-1) of them are shown to be sufficient.Comment: RevTeX, 4+ pages, 2 figures, journal version includes an Appendix and slightly enlarged introduction and conclusion