Multipartite entanglement detection via generalized Wigner-Yanase skew information

TL;DR

This paper introduces new inequalities based on generalized Wigner-Yanase skew information to detect and classify multipartite entanglement and $k$-nonseparability in quantum systems, revealing entanglement undetectable by previous methods.

Contribution

The paper develops novel entanglement criteria using generalized Wigner-Yanase skew information, providing more refined hierarchical detection of multipartite entanglement.

Findings

Detects $k$-nonseparability and $k$-partite entanglement in quantum systems.

Reveals entanglement undetected by existing methods.

Provides examples illustrating the effectiveness of the criteria.

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.