Multipartite k‐Entanglement Measures and Coherence

Abstract

Characterizing the entanglement in multipartite quantum systems remains a central challenge in the theory of quantum entanglement. We establish a comprehensive framework for constructing k$k$ ‐entanglement measures by leveraging bipartite entanglement measures and general m$m$ ‐entanglement measures ( m≤k$m \le k$ ) with arithmetic and geometric averaging schemes. Numerical examples demonstrate that these measures outperform the existing ones, such as k$k$ ‐ME concurrence, geometric mean (k‐GM) concurrence, and the generalized k$k$ ‐entanglement measure Γk-ME$\Gamma _{k\text{-ME}}$ by inducing distinct entanglement orderings and offering superior resolution. Furthermore, we reveal the operational relationship between the k$k$ ‐entanglement and the local quantum coherence, verifying that the persistence of entanglement is intrinsically constrained by the system's capacity to maintain the local coherence. Finally, to overcome the inherent limitation of the conventional three‐tangle τ3$\tau _3$ in characterizing the genuine multipartite entanglement of the GHZ‐W mixed states, we design a novel GME measure. Numerical results confirm that this measure effectively eliminates the detection blind spots where τ3$\tau _3$ vanishes, providing a complete and practical mathematical tool for the quantitative analysis of genuine multipartite quantum correlations.