Quantum coherence and correlation measures based on affinity

Abstract: Coherence and correlation are key features of the quantum system. Quantifying these quantities are astounding task in the framework of resource theory of quantum information processing. In this article, we identify an affinity-based metric to quantify closeness between two states. Using this metric, we introduce a valid quantum coherence measure. It is shown that the affinity based coherence measure is bounded by that based on fidelity and trace distance. Further, we propose a bipartite quantum correlation measure based on the affinity metric. The connection between the quantum correlation of states and its local coherence is established. The measure of quantumness in terms of difference of bipartite coherence and corresponding product state coherence is also identified. Finally, we interpret the operational meaning of the affinity based coherence as an upper bound of interferometric power of the quantum state.