Separability criteria based on Bloch representation of density matrices

  • Hui ZhaoEmail author
  • Mei-Ming Zhang
  • NaiHuan Jing
  • Zhi-Xi Wang


We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for separability under partition of tripartite and four-partite quantum states. Moreover, based on the norms of the correlation tensors, we obtain the separability criteria by matrix method. Using detailed examples, our results are seen to be able to detect more entangled states than previous studies. Finally, necessary conditions of separability for multipartite systems are given under arbitrary partition.


Separability Bloch vector Entanglement 



This work is supported by the National Natural Science Foundation of China under Grant Nos. 11101017, 11531004, 11726016 and 11675113, and Simons Foundation under Grant No. 523868, Key Project of Beijing Municipal Commission of Education (KZ201810028042).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Applied SciencesBeijing University of TechnologyBeijingChina
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  3. 3.School of Mathematical SciencesCapital Normal UniversityBeijingChina

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