Polygamy of entanglement of assistance: duality monogamy inequality for entanglement

“Monogamy of entanglement” bounds bipartite sharing of entanglement and reveals a complete absence of sharing either entanglement or correlations beyond a single maximally entangled pair. This taboo on sharing entanglement or correlations is a peculiarly quantum feature and has important implications for the security of quantum key distribution. We prove that the monogamy upper bound is in fact a lower bound for distribution of entanglement of assistance to a target pair, thereby establishing a close link between sharing entanglement vs. entanglement of assistance.