Superadditivity of Convex Roof Coherence Measures in Multipartite System

Abstract: In this paper, we investigate the convex roof measure of quantum coherence, with a focus on their superadditive properties. We propose sufficient conditions and establish a framework for coherence superadditivity in tripartite and multipartite systems. Through theoretical derivation, the relevant theorems are given. These results not only expand our understanding of the superadditivity of pure and mixed states but also characterize the conditions under which the superadditivity relations reach equality. Finally, the proposed methods and conclusions are verified through representative examples, providing new theoretical insights into the distribution of quantum coherence in multi-part systems.