TY - JOUR
T1 - Tensor rank of the tripartite state |W n
AU - Yu, Nengkun
AU - Chitambar, Eric
AU - Guo, Cheng
AU - Duan, Runyao
PY - 2010/1/15
Y1 - 2010/1/15
N2 - 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).
AB - 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).
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U2 - 10.1103/PhysRevA.81.014301
DO - 10.1103/PhysRevA.81.014301
M3 - Article
AN - SCOPUS:74549157343
SN - 1050-2947
VL - 81
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 1
M1 - 014301
ER -