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Chin. Phys. B, 2008, Vol. 17(8): 2795-2799    DOI: 10.1088/1674-1056/17/8/008
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Genuine tripartite entanglement and quantum phase transition

Yu Chang-Shui(于长水), Song He-Shan(宋鹤山), and Cui Hai-Tao(崔海涛)
Department of Physics, Dalian University of Technology, Dalian 116024, China
Abstract  A new simplified formula is presented to characterize genuine tripartite entanglement of $(2\otimes 2\otimes n)$-dimensional quantum pure states. The formula turns out equivalent to that given in (Quant. Inf. Comp. 7(7) 584 (2007)), hence it also shows that the genuine tripartite entanglement can be described only on the basis of the local $(2\otimes 2)$-dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang (Phys. Rev. A 71 030302(R) (2005)) are reconsidered by employing the formula. The results show that a discontinuity in the first derivative of the formula or in the formula itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously different from the concurrence.
Keywords:  entanglement measure      tripartite entanglement      quantum phase transition  
Received:  10 November 2007      Revised:  26 March 2008      Accepted manuscript online: 
PACS:  03.65.Ud (Entanglement and quantum nonlocality)  
  75.10.Jm (Quantized spin models, including quantum spin frustration)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10747112 and 10575017).

Cite this article: 

Yu Chang-Shui(于长水), Song He-Shan(宋鹤山), and Cui Hai-Tao(崔海涛) Genuine tripartite entanglement and quantum phase transition 2008 Chin. Phys. B 17 2795

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