Quantifying multilevel coherence and multipartite correlation based on $\alpha$-affinity

Compared with quantum coherence, multilevel quantum coherence offers a hierarchical classification that enables a more refined characterization. In this paper, we investigate multilevel coherence and introduce two $\alpha$-affinity-based indicators to quantify it, which exhibit a range of desirable properties. We further define $\alpha$-affinity-based indicators of multipartite correlation and analyze their properties. Finally, we explore and establish the relationship between these multilevel coherence indicators and the multipartite correlation indicators, thereby clarifying the connection between multilevel coherence and multipartite correlation.