%0 Journal Article
%T The Tensor Rank of the Tripartite State $\ket{W}^{\otimes n}$}
%A Nengkun Yu
%A Eric Chitambar
%A Cheng Guo
%A Runyao Duan
%J Physics
%D 2009
%I arXiv
%R 10.1103/PhysRevA.81.014301
%X Tensor rank refers to the number of product states needed to express a given multipartite quantum state. Its non-additivity as an entanglement measure has recently been observed. In this note, we estimate the tensor rank of multiple copies of the tripartite state $\ket{W}=\tfrac{1}{\sqrt{3}}(\ket{100}+\ket{010}+\ket{001})$. Both an upper bound and a lower bound of this rank are derived. In particular, it is proven that the tensor rank of $\ket{W}^{\otimes 2}$ is seven, thus resolving a previously open problem. Some implications of this result are discussed in terms of transformation rates between $\ket{W}^{\otimes n}$ and multiple copies of the state $\ket{GHZ}=\tfrac{1}{\sqrt{2}}(\ket{000}+\ket{111})$.
%U http://arxiv.org/abs/0910.0986v3