Genuine multipartite entanglement from a thermodynamic perspective

Among the various types of quantum entanglement, the most fascinating and interesting one is genuine entanglement undoubtedly. In this paper, the unique genuine decomposition theorem with respect to any pure state is given and the relations between battery capacity gap and ergtropic gap are studied. By exploiting the battery capacity of multipartite systems, we introduce a vector-valued genuine measure compared with other existing measures and find that the one is superior to some other existing measures in confirming whether the deterministic LOCC transformation between two multipartite pure states is prohibited. Through some proper constructions, one can derive many GME measures. We also give the explicit expression of bipartite battery capacity gap with respect to mixed states by the convex roof extension and investigate some monogamy relations related to the battery capacity gap.