中国物理B ›› 2008, Vol. 17 ›› Issue (8): 2795-2799.doi: 10.1088/1674-1056/17/8/008

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Genuine tripartite entanglement and quantum phase transition

于长水, 宋鹤山, 崔海涛   

  1. Department of Physics, Dalian University of Technology, Dalian 116024, China
  • 收稿日期:2007-11-10 修回日期:2008-03-26 出版日期:2008-08-20 发布日期:2008-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10747112 and 10575017).

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)   

  1. Department of Physics, Dalian University of Technology, Dalian 116024, China
  • Received:2007-11-10 Revised:2008-03-26 Online:2008-08-20 Published:2008-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10747112 and 10575017).

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摘要： 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 (\wx{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 (\wx{Phys. Rev. {\rm 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.

关键词: entanglement measure, tripartite entanglement, quantum phase transition

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.

Key words: entanglement measure, tripartite entanglement, quantum phase transition

中图分类号:  (Entanglement and quantum nonlocality)

  • 03.65.Ud
75.10.Jm (Quantized spin models, including quantum spin frustration)