Entanglement in the symmetric subspace: mapping multipartite to bipartite states

Abstract: We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an N-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves separability and allows to characterize the entanglement of the original multipartite state. In particular, we provide several bounds to estimate the symmetric tensor rank and geometric measure of entanglement. Finally, we reveal the existence of entangled symmetric subspaces, where all bipartite states are entangled.