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Tensor rank of the tripartite state |Wn

Source: Phys. Rev. A 81, 014301 (2010); doi:10.1103/PhysRevA.81.014301

Published 15 January 2010

PACS
  • 03.67.Mn
    Entanglement measures, witnesses, and other characterizations (quantum information)
  • 03.65.-w
    Quantum mechanics
  • YEAR: 2010
PUBLICATION DATA
Publisher:
AIP is a member of CrossRef APS
Nengkun Yu,1 Eric Chitambar,2 Cheng Guo,1 and Runyao Duan1
1State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China and Centre for Quantum Computation and Intelligent Systems (QCIS), Faculty of Engineering and Information Technology, University of Technology, Sydney, New South Wales 2007, Australia
2Physics Department, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, USA
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=(1/(sqrt(3)))(|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 |W2 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=(1/(sqrt(2)))(|000+|111). ©2010 The American Physical Society
History: Received 23 October 2009; published 15 January 2010
Permalink: http://link.aps.org/abstract/PRA/v81/e014301
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