Structure of Resource Theory of Block Coherence

Abstract: Emerging from the superposition principle, the resource theory of coherence plays a crucial role in many information-processing tasks. Recently, a generalization to this resource theory was investigated with respect to arbitrary positive operator valued measurement (POVM) based on Naimark's dilation theorem. Here, we introduce the notion of Block Incoherent Operations (BIO), Strictly Block Incoherent Operations (SBIO) and Physically Block Incoherent Operations (PBIO) and provide an analytical expression for Kraus operators of these operations to have a better understanding of the resource theory of block coherence which in turn gives a more clear picture of POVM based resource theory of coherence. A dilation theorem corresponding to SBIO has been introduced to enlighten the proper physical interpretation of this operation. These free operations will be helpful in finding out the conditions of state transformations and could be implemented in various protocols. For a transparent view of this resource theory, we have successfully introduced the concept of state transformation under SBIO.