Generalized Entanglement Monogamy and Polygamy Relations for N -Qubit Systems

Abstract

We investigate the generalized monogamy and polygamy relations $N$-qubit systems. We give a general upper bound of the $\alpha$th ($0\le \alpha \le 2$) power of concurrence for $N$-qubit states. The monogamy relations satisfied by the $\alpha$th ($0\le \alpha \le 2$) 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 $AB{C}_1$ 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.