Quantifying multilevel coherence and multipartite correlation based on $\hat{I}\pm$-affinity

Abstract

Unlike standard quantum coherence, multilevel quantum coherence provides a hierarchical structure that enables a more refined characterization of quantum superposition. In this paper, we investigate multilevel coherence and introduce two $\hat{I}\pm$-affinity-based indicators to quantify it, both of which satisfy several desirable properties. We further define $\hat{I}\pm$-affinity-based indicators for multipartite correlation and analyze their properties. Finally, we establish relationships between these multilevel coherence indicators and the multipartite correlation indicators.