Monogamy of entanglement of maximal dimension

TL;DR

This paper generalizes the monogamy of entanglement to higher-dimensional quantum states using G-concurrence, deriving an inequality analogous to the CKW inequality for qudits and establishing bounds for mixed states.

Contribution

It introduces a monogamy inequality for entanglement in higher-dimensional systems using G-concurrence, extending previous qubit-based results.

Findings

Derived a monogamy inequality for $ ext{C}^d imes ext{C}^d imes ext{C}^d$ states.

Established an upper bound for G-concurrence in bipartite qudit mixed states.

Demonstrated the inequality's consistency with known qubit results.

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.