Entanglement in the symmetric subspace: Mapping multipartite to bipartite states

This is the authors' abstract. We don't add key points for this paper.

We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>N</a:mi> </a:math> -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 establish a connection between the border rank and the Schmidt rank, and derive lower bounds on entanglement measures. Finally, we reveal the existence of entangled symmetric subspaces, where all bipartite states are entangled.