Monogamy of entanglement of maximal dimension

Abstract

In the present paper, a trade off of sharing of entanglement between subsystems of a higher dimensional quantum state is derived. It is presented in terms of an inequality which is analogous to the Coffman-Kundu-Wootters inequality that succinctly describes monogamy of entanglement in $\mathcal{C}^2\otimes \mathcal{C}^2\otimes \mathcal{C}^2$ dimensional pure state. To derive the monogamy inequality in $\mathcal{C}^d\otimes \mathcal{C}^d\otimes \mathcal{C}^d$ dimension, G-concurrence measure of entanglement is considered as a measure of entanglement of maximal dimension. The approach of the present paper incidentally points towards a rigorous framework which enables us to obtain an upper bound of G-concurrence of a bipartite qudit mixed state. Obtained upper bound of G-concurrence is then shown to satisfy a monogamy relation.