Local Interaction Information and Local Quantum Mutual Information in Multiparty Systems

Quantum correlation in bipartite systems has been extensively studied, and in recent years, people have been interested in the study of multipartite systems. Studying quantum correlations in local multipartite systems has also become a hot topic. In this paper, we define the local bipartite conditional mutual information, and further give the definitions of local multipartite interaction (common) information and local genuinely multipartite quantum mutual information. Then, we mainly study some properties and special relations of local genuinely multipartite quantum mutual information satisfaction. A special property that is different from the nonlocal case is that the local genuinely multipartite quantum mutual information may change under the local unitary operation. This is caused by the fact that the unitary operation may change the position of the particles.