# Generalized Entanglement Monogamy and Polygamy Relations for N -Qubit Systems

## TL;DR

This paper establishes generalized monogamy and polygamy relations for entanglement measures like concurrence and negativity in N-qubit systems, providing bounds and inequalities that describe how entanglement is distributed among subsystems.

## Contribution

It introduces a general upper bound for the αth power of concurrence in N-qubit states and derives new monogamy and polygamy inequalities for various partitions, extending previous entanglement distribution constraints.

## Key findings

- Derived a general upper bound for the αth power of concurrence.
- Established monogamy relations for N-qubit pure states under specific partitions.
- Extended results to negativity, providing similar entanglement constraints.

## Abstract

We investigate the generalized monogamy and polygamy relations $N$-qubit systems. We give a general upper bound of the $\alpha$th ($0\leq\alpha\leq2$) power of concurrence for $N$-qubit states. The monogamy relations satisfied by the $\alpha$th ($0\leq\alpha\leq2$) power of concurrence are presented for $N$-qubit pure states under the partition $AB$ and $C_1 . . . C_{N-2}$, as well as under the partition $ABC_1$ and $C_2\cdots C_{N-2}$. These inequalities give rise to the restrictions on entanglement distribution and the trade off of entanglement among the subsystems. Similar results are also derived for negativity.