Construction and characterization of measures in block coherence resource theory

TL;DR

This paper develops new methods for constructing and comparing measures of block coherence in quantum resource theory, providing theoretical insights and applications to quantum dynamics.

Contribution

It introduces two universal methods for constructing block coherence measures and compares their properties through theoretical proofs and numerical examples.

Findings

Proposed two families of block coherence measures based on $ ext{α}$-$z$ Rényi and Tsallis entropies.

Established inequalities constraining the values of different coherence measures.

Demonstrated the role of coherence measures in quantum dynamics via the Kominis master equation.

Abstract

Quantum coherence, as a direct manifestation of the quantum superposition principle, is a crucial resource in quantum information processing. Block coherence resource theory generalizes the traditional coherence framework by defining coherence via a set of orthogonal projectors. Within this framework, we investigates the construction and comparison of block coherence measures. First, we propose two universal methods for constructing coherence measures and introduce a two-parameter family of measures based on the $\alpha$-$z$ R\'enyi relative entropy and a family of measures based on the Tsallis relative operator entropy. Second, through theoretical proofs and numerical counterexamples, we compares the ordering relations and numerical magnitudes among different block coherence measures and establishes a series of universal numerical inequalities to constrain their values. Besides, we also use $C_{\alpha,1}$ to show the role of coherence in complex dynamic evolution of the Kominis master equation that includes recombination reactions.