The block-coherence measures and the coherence measures based on positive-operator-valued measures

Abstract: We mainly study the block-coherence measures based on resource theory of block-coherence and the coherence measures based on positive-operator-valued measures (POVM). Several block-coherence measures including a block-coherence measure based on maximum relative entropy, the one-shot block coherence cost under the maximally block-incoherent operations, and a coherence measure based on coherent rank have been introduced and the relationships between these block-coherence measures have been obtained. We also give the definition of the maximally block-coherent state and describe the deterministic coherence dilution process by constructing block-incoherent operations. Based on the POVM coherence resource theory, we propose a POVM-based coherence measure by using the known scheme of building POVM-based coherence measures from block-coherence measures, and the one-shot block coherence cost under the maximally POVM-incoherent operations. The relationship between the POVM-based coherence measure and the one-shot block coherence cost under the maximally POVM-incoherent operations is analysed.