Relative entropy of entanglement for certain multipartite mixed states

We prove conjectures on the relative entropy of entanglement (REE) for two families of multipartite qubit states. Thus, analytic expressions of REE for these families of states can be given. The first family of states are composed of mixture of some permutation-invariant multi-qubit states. The results generalized to multi-qudit states are also shown to hold. The second family of states contain D"ur’s bound entangled states. Along the way, we have discussed the relation of REE to two other measures: robustness of entanglement and geometric measure of entanglement, slightly extending previous results.