Multipartite entanglement detection via generalized Wigner–Yanase skew information

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. We deduce the upper bounds on the generalized Wigner–Yanase skew information of k-separable states and k-producible states in arbitrary dimensional multipartite quantum systems. And based on the upper bounds, we develop two different approaches in form of simple 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. Some well-known entanglement criteria are the special cases of our criteria. We illustrate the significance of our criteria by showing that they can reveal k-nonseparability and k-partite entanglement undetectable by well-known criteria through several typical examples, and their advantages over well-known criteria. •Explore multipartite entanglement via generalized Wigner–Yanase skew information.•Present criteria for detecting k-partite entanglement andk-nonseparability.•Some previous entanglement criteria are the special cases of our criteria.•We detect more k-partite entanglement and k-nonseparability than previous methods.•Several typical examples are provided.