Upper bound of holographic entanglement entropy combinations

A bstract In this work, we develop a systematic formalism to evaluate the upper bound of a large family of holographic entanglement entropy combinations when fixing n subsystems and fine-tuning one other subsystem. The upper bound configurations and values of these entropy combinations can be derived and classified. The upper bound of these entropy combinations reveals holographic n + 1-partite entanglement that n fixed subsystems participate in. In AdS 3 /CFT 2 , AdS 4 /CFT 3 , and even higher-dimensional holography, one can, in principle, find different formulas of upper bound values, reflecting the fundamental difference in entanglement structure in different dimensions.