Genuine multipartite entanglement measure based on triangle structure

Quantifying genuine entanglement is a crucial task in quantum information theory. Very recently, a genuine three-qubit entanglement measure induced by the area of concurrence triangle was proposed in [Phys. Rev. Lett., 127, 040403]. In this work, we show that this scenario is also valid for any other entanglement measure and system with any dimension. Moreover, in light of the triangle structure, we give genuine entanglement measures for any four-partite system via the complete tripartie entanglement measure and the triangle measure respectively.