A geometric representation of entanglement

In this paper, we introduce a novel way of witnessing entanglement in quantum systems. This geometrical approach will enable us to differentiate systems with high quantum correlation from systems with low quantum correlation. We will show using this geometrical approach to quantum entanglement; one can address the entanglement between specific parts of the quantum network without the necessity to calculate all pairwise entanglement between nodes in the network. We will also show that for particular quantum networks, this geometrical approach will be the geometrical realization of squashed entanglement. Our approach is inspired by Schumacher's singlet state triangle inequality, that used an information geometry-based entropic distance, however, unlike Schumacher, who uses classical entropy, we will use von Neumann entropy to reach a new inequality and then will generalize this inequality using entropic areas and volumes and higher dimensional volumes for multipartite quantum systems.