Characterizing entanglement shareability and distribution in $N$-partite systems

TL;DR

This paper investigates the shareability and distribution of entanglement in multipartite quantum systems, introducing hierarchical monogamy relations for generalized entanglement measures and demonstrating their advantages over traditional measures.

Contribution

It establishes hierarchical monogamy relations for $G_q$-concurrence in $N$-qubit states and shows their superiority over squared concurrence in multilevel systems.

Findings

Hierarchical monogamy relations for $G_q$-concurrence are proven.

$G_q$-concurrence better witnesses entanglement in multilevel systems.

Monogamy property of $G_q$-concurrence is stronger than that of concurrence.

Abstract

Exploring the shareability and distribution of entanglement possesses fundamental significance in quantum information tasks. In this paper, we demonstrate that the square of bipartite entanglement measures $G_q$-concurrence, which is the generalization of concurrence, follows a set of hierarchical monogamy relations for any $N$-qubit quantum state. On the basis of these monogamy inequalities, we render two kinds of hierarchical indicators that exhibit evident advantages in the capacity of witnessing entanglement. Moreover, we show an analytical relation between $G_q$-concurrence and concurrence in $2\otimes d$ systems. Furthermore, we rigorously prove that the monogamy property of squared $G_q$-concurrence is superior to that of squared concurrence in $2\otimes d_2\otimes d_3\otimes\cdots\otimes d_N$ systems. In addition, several concrete examples are provided to illustrate that for multilevel systems, the squared $G_q$-concurrence satisfies the monogamy relation, even if the squared concurrence does not. These results better reveal the intriguing characteristic of multilevel entanglement and provide critical insights into the entanglement distribution within multipartite quantum systems.