Tensor rank of the tripartite state

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Journal Article
Physical Review A - Atomic, Molecular, and Optical Physics, 2010, 81 (1)
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Tensor rank refers to the number of product states needed to express a given multipartite quantum state. Its nonadditivity as an entanglement measure has recently been observed. In this Brief Report, we estimate the tensor rank of multiple copies of the tripartite state |W=13(|100+|010+|001). Both an upper bound and a lower bound of this rank are derived. In particular, it is proven that the rank of |W 2 is 7, thus resolving a previously open problem. Some implications of this result are discussed in terms of transformation rates between |Wn and multiple copies of the state |GHZ=12(|000+|111). © 2010 The American Physical Society.
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