Abstract
The relative entropy of entanglement is defined in terms of the relative entropy between an entangled state and its closest separable state (CSS). Given a multipartite-state on the boundary of the set of separable states, we find an explicit expression for all the entangled states for which this state is a CSS. Our formula holds for multipartite states in all dimensions. For the bipartite case of two qubits, our formula reduce to the one given by Miranowicz and Ishizaka [Phys. Rev. A 78, 032310 (2008)].
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