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Separability Criteria Based on the Weyl Operators |
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| Authors: | Xiaofen Huang Tinggui Zhang Ming-Jing Zhao Naihuan Jing |
| Affiliation: | 1.School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China;2.Key Laboratory of Data Science and Smart Education, Ministry of Education, Hainan Normal University, Haikou 571158, China;3.School of Science, Beijing Information Science and Technology University, Beijing 100192, China;4.Department of Mathematics, Shanghai University, Shanghai 200444, China;5.Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA |
| Abstract: | Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We show that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation. |
| Keywords: | separability Weyl operators Bloch representation correlation matrix quantum teleportation |