Monogamy of $\alpha$th Power Entanglement Measurement in Qubit Systems

TL;DR

This paper explores the monogamy properties of the $oldsymbol{ extit{ extalpha}}$th power of entanglement measures in qubit systems, deriving new inequalities and bounds to better understand entanglement distribution.

Contribution

It introduces new monogamy relations for the $ extalpha$th power of negativity and entanglement of formation, and compares different entanglement measures in qubit systems.

Findings

Derived monogamy relations for negativity and convex-roof negativity.

Provided a tighter bound for hierarchical monogamy inequality of entanglement of formation.

Showed that GHZ and W states can distinguish the $ extalpha$th power of concurrence for $0< extalpha<2$.

Abstract

In this paper, we study the $\alpha$th power monogamy properties related to the entanglement measure in bipartite states. The monogamy relations related to the $\alpha$th power of negativity and the Convex- Roof Extended Negativity are obtained for N-qubit states. We also give a tighter bound of hierarchical monogamy inequality for the entanglement of formation. We find that the GHZ state and W state can be used to distinguish the $\alpha$th power the concurrence for $0<\alpha<2$. Furthermore, we compare concurrence with negativity in terms of monogamy property and investigate the difference between them.