Tensor rank of the tripartite state |W n

Nengkun Yu, Eric Chitambar, Cheng Guo, Runyao Duan

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish (US)
Article number014301
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number1
StatePublished - Jan 15 2010
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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