Family of One‐Parameter Multipartite Entanglement Measures

ABSTRACT Multipartite entanglement is widely recognized as a fundamental resource for various quantum protocols, including those in quantum communication and quantum computing. However, a unified characterization of multipartite entanglement remains elusive. In this paper, we introduce ‐Concentratable Entanglements, a one‐parameter family of measures for multipartite entanglement. This framework generalizes the Concentratable Entanglements framework, recovering the original measure at the limit of . We prove that ‐Concentratable Entanglements is a valid entanglement measure satisfying local operations and classical communication monotonicity and continuity. While linear cluster states are known to exhibit higher concentratable entanglements than Greenberger‐Horne‐Zeilinger (GHZ) states at the specific point , To demonstrate the versatility of the ‐Concentratable Entanglements framework, we performed a comprehensive analysis of several paradigmatic multipartite states. Our comparison of ‐qubit GHZ and W states shows that the measure can distinguish them well, while the investigation of the 4‐partite star network illustrates the role of as a tunable parameter for probing structural subtleties. Most significantly, by analyzing the 4‐qubit linear cluster state () and the 4‐qubit GHZ states, we find that the hierarchical ordering is a robust feature in the parameter range .