A note on entanglement classification for tripartite mixed states

Hui  Zhao; Yu-Qiu  Liu; Zhi-Xi  Wang; Shao-Ming Fei

doi:10.14311/AP.2022.62.0222

Authors

Hui Zhao Beijing University of Technology, Faculty of Science, Beijing 100124, China
Yu-Qiu Liu Beijing University of Technology, Faculty of Science, Beijing 100124, China
Zhi-Xi Wang Capital Normal University, School of Mathematical Sciences, Beijing 100037, China
Shao-Ming Fei Capital Normal University, School of Mathematical Sciences, Beijing 100037, China

DOI:

https://doi.org/10.14311/AP.2022.62.0222

Keywords:

bell inequalities, separability, principal basis

Abstract

We study the classification of entanglement in tripartite systems by using Bell-type inequalities and principal basis. By using Bell unctions and the generalized three dimensional Pauli operators, we present a set of Bell inequalities which classifies the entanglement of triqutrit fully separable and bi-separable mixed states. By using the correlation tensors in the principal basis representation of density matrices, we obtain separability criteria for fully separable and bi-separable 2 ⊗ 2 ⊗ 3 quantum mixed states. Detailed example is given to illustrate our criteria in classifying the tripartite entanglement.

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