Multipartite entanglement detection via generalized Wigner-Yanase skew information
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912270269808640 |
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| author | Hong, Yan Xing, Yabin Gao, Limin Gao, Ting Yan, Fengli |
| author_facet | Hong, Yan Xing, Yabin Gao, Limin Gao, Ting Yan, Fengli |
| contents | The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory. In this paper, we investigate $k$-nonseparability and $k$-partite entanglement of $N$-partite quantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang $et$ $al$. [\href{https://doi.org/10.1103/PhysRevA.106.052401 }{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information. Any violation of these inequalities by a quantum state reveals its $k$-nonseparability or $k$-partite entanglement, so these inequalities present the hierarchic classifications of $k$-nonseparability or $k$-partite entanglement for all $N$-partite quantum states from $N$-nonseparability to $2$-nonseparability or from $2$-partite entanglement to $N$-partite entanglement, which are more refined than well-known ways.
It is shown that our results reveal some $k$-nonseparability and $k$-partite entanglement that remain undetected by other methods, and these are illustrated through some examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_11034 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multipartite entanglement detection via generalized Wigner-Yanase skew information Hong, Yan Xing, Yabin Gao, Limin Gao, Ting Yan, Fengli Quantum Physics The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory. In this paper, we investigate $k$-nonseparability and $k$-partite entanglement of $N$-partite quantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang $et$ $al$. [\href{https://doi.org/10.1103/PhysRevA.106.052401 }{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information. Any violation of these inequalities by a quantum state reveals its $k$-nonseparability or $k$-partite entanglement, so these inequalities present the hierarchic classifications of $k$-nonseparability or $k$-partite entanglement for all $N$-partite quantum states from $N$-nonseparability to $2$-nonseparability or from $2$-partite entanglement to $N$-partite entanglement, which are more refined than well-known ways. It is shown that our results reveal some $k$-nonseparability and $k$-partite entanglement that remain undetected by other methods, and these are illustrated through some examples. |
| title | Multipartite entanglement detection via generalized Wigner-Yanase skew information |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2309.11034 |