The Tensor Rank of the Tripartite State $\ketW^\otimes n$. Yu, N., Chitambar, E., Guo, C., & Duan, R. Physical Review A - Atomic, Molecular, and Optical Physics, 81(1):3-5, 10, 2009. ![The Tensor Rank of the Tripartite State $\ketW^\otimes n$ [link]](https://bibbase.org/img/filetypes/link.svg "link")
Website doi abstract bibtex 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 $\ketW=\tfrac1\sqrt3(\ket100+\ket010+\ket001)$. Both an upper bound and a lower bound of this rank are derived. In particular, it is proven that the tensor rank of $\ketW^\otimes 2$ is seven, thus resolving a previously open problem. Some implications of this result are discussed in terms of transformation rates between $\ketW^\otimes n$ and multiple copies of the state $\ketGHZ=\tfrac1\sqrt2(\ket000+\ket111)$.
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title = {The Tensor Rank of the Tripartite State $\ketW^\otimes n$},
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abstract = {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 $\ketW=\tfrac1\sqrt3(\ket100+\ket010+\ket001)$. Both an upper bound and a lower bound of this rank are derived. In particular, it is proven that the tensor rank of $\ketW^\otimes 2$ is seven, thus resolving a previously open problem. Some implications of this result are discussed in terms of transformation rates between $\ketW^\otimes n$ and multiple copies of the state $\ketGHZ=\tfrac1\sqrt2(\ket000+\ket111)$.},
bibtype = {article},
author = {Yu, Nengkun and Chitambar, Eric and Guo, Cheng and Duan, Runyao},
doi = {10.1103/PhysRevA.81.014301},
journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
number = {1}
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