Multipartite entanglement detection via generalized Wigner-Yanase skew information

• URL: http://arxiv.org/abs/2309.11034v1
• Date: Wed, 20 Sep 2023 03:30:15 GMT
• Title: Multipartite entanglement detection via generalized Wigner-Yanase skew information
• Authors: Yan Hong, Yabin Xing, Limin Gao, Ting Gao, Fengli Yan
• Abstract summary: The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory. We develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the Wigner-Yanase skew information. Our results reveal some $k$-nonseparability and $k$-partite entanglement that remain undetected by other methods.
• Score: 7.222232547612572
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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