Entanglement monogamy relations of qubit systems

We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the $\alpha \text{th}$ power of concurrence and entanglement of formation are presented for $N$-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.

Figure 1

Solid line: ${\tau }_{\alpha }^C\left(\right|W\rangle )$ as a function of $\alpha$ ($\alpha \ge 2$); dashed line: ${\tau }_{\alpha }^E\left(\right|W\rangle )$ as a function of $\alpha$ ($\alpha \ge \sqrt{2}$).

Figure 2

The lower bound of $E_a\left({\rho }_{AB}\right)$ for state (26) with $\alpha \ge \sqrt{2}$.