Genuine multipartite coherence under correlated noisy channels in N-partite systems

In this paper, we define the genuine multipartite coherence and genuine multipartite average coherence, discuss their properties and investigative the relationship between them and other quantum resources. Firstly, we prove that the genuine multipartite coherence can be represented by interaction information, and it can determine whether genuine multipartite discord exists. Secondly, comparing the global coherence and genuine multipartite coherence in noisy channels with different correlation strengths, the global coherence and genuine multipartite coherence are more stable with the increasing correlation strengths, and genuine multipartite coherence is more stable than global coherence. Finally, we find that the difference between genuine multipartite coherence and genuine multipartite average coherence can be expressed by quantum discord, and the genuine multipartite coherence is always greater than or equal to the genuine multipartite entanglement. For the tripartite pure states, we provide some trade-off relations between the total correlation, classical correlation, and quantum correlations.