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

TL;DR

This paper explores various measures of block-coherence and POVM-based coherence within resource theory, establishing relationships and defining key states and processes in quantum coherence resource management.

Contribution

It introduces new block-coherence measures, defines maximally block-coherent states, and extends coherence measures to POVM-based frameworks, analyzing their interrelations.

Findings

Several new block-coherence measures are proposed.

Relationships between different block-coherence measures are established.

A POVM-based coherence measure is constructed and analyzed.

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.