  This work aims to understand the monogamy of quantum entanglement from a
geometrical point of view. By regarding quantum entanglement as a geometrical
structure on the state space of quantum systems and attributing all
entanglement related properties as emergent from this geometry of entanglement,
we assume there exists a genuine general monogamous relation of quantum
entanglement w.r.t. a correspondent genuine entanglement measure Q* which
possesses an underlying geometrical origin. We speculate that the monogamous
relations w.r.t. an entanglement measure Q can be understood by comparing the
different dimension dependencies of the measure Q and Q*. We gave evidences of
our conjecture by readdressing two observed properties of the monogamy
relations from this geometrical standpoint. Besides the phenomenal explanation
of the monogamy of entanglement, we also discussed a fibre bundle structure
based candidate solution for the geometry of entanglement and explained how
this idea is related to the ER=EPR conjecture and other interesting quantum
information processing problems including monogamy of entanglement,
entanglement distillation, bound entanglement and activation, and entanglement
catalyst.
