Frontiers of Physics in China

, Volume 3, Issue 3, pp 250–257 | Cite as

Concurrence vectors for entanglement of high-dimensional systems

  • You-Quan Li
  • Guo-Qiang Zhu
Research Article


The concurrence vectors are proposed by employing the fundamental representation of A n Lie algebra, which provides a clear criterion to evaluate the entanglement of bipartite systems of arbitrary dimension. Accordingly, a state is separable if the norm of its concurrence vector vanishes. The state vectors related to SU(3) states and SO(3) states are discussed in detail. The sign situation of nonzero components of concurrence vectors of entangled bases presents a simple criterion to judge whether the whole Hilbert subspace spanned by those bases is entangled, or there exists an entanglement edge. This is illustrated in terms of the concurrence surfaces of several concrete examples.


entanglement concurrence high-dimensional Hilbert space 

PACS numbers

03.67.Mn 03.65.Ud 03.65.Ca 


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Copyright information

© Higher Education Press 2008

Authors and Affiliations

  1. 1.Zhejiang Institute of Modern PhysicsZhejiang UniversityHangzhouChina

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