Geometrical Equivalence Of Entanglement

n this paper, we propose a novel way for coarse-graining entanglement in quantum networks; this unique 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’ssinglet state triangle inequality, which used an information geometry-based entropic distance, but unlike Schumacher, which used classical entropy, we will not only use proper quantum entropy to reach a new inequality but will also generalize this inequality to inequalities for areas and volumes and higher dimensional volumes for multipartite quantum systems.