Block-coherence measures and coherence measures based on positive-operator-valued measures

We study block-coherence measures based on the resource theory of block-coherence and coherence measures based on positive-operator-valued measures(POVM).Several blockcoherence measures are presented,including the block-coherence measure based on maximum relative entropy,the one-shot block-coherence cost under maximally block-incoherent operations,and the coherence measure based on coherent rank.Their relationships are obtained.Moreover,we describe the deterministic coherence dilution process by constructing blockincoherent operations.Based on the POVM coherence resource theory,we also propose two coherence measures and analyze their relationship.