Separable decompositions of bipartite mixed states

  • Jun-Li Li
  • Cong-Feng Qiao


We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8:1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then, we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.


Entanglement of mixed states Separability criterion Bloch vector Matrix decomposition 



This work was supported in part by the Ministry of Science and Technology of the Peoples’ Republic of China (2015CB856703); by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB23030100); and by the National Natural Science Foundation of China (NSFC) under the Grants 11375200 and 11635009.


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Authors and Affiliations

  1. 1.Department of PhysicsUniversity of the Chinese Academy of SciencesBeijingChina
  2. 2.Key Laboratory of Vacuum PhysicsUniversity of Chinese Academy of SciencesBeijingChina

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