Dual monogamy inequality for entanglement

Abstract

We establish duality for monogamy of entanglement: whereas monogamy of entanglement inequalities provide an upper bound for bipartite sharability of entanglement in a multipartite system, as quantified by linear entropy, we prove that the same quantity (namely, linear entropy) provides a lower bound for distribution of bipartite entanglement in a multipartite system. Our theorem for monogamy of entanglement is used to establish relations between bipartite entanglement that separate one qubit from the rest versus separating two qubits from the rest.