On entanglement as a relation

Bob Coecke

Xue‐Na Zhu, Shao-Ming Fei

We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the $\ensuremath{\alpha}\text{th}$ 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.

Yanying Liang, Zhu‐Jun Zheng, Chuan-Jie Zhu

We investigate monogamy relations related to the Rényi-$α$ entanglement and polygamy relations related to the Rényi-$α$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $μ\geqslant2$, and polygamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement of assistance with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $0\leqμ\leq1$. These relations are shown to be tighter than the existing ones.

Gregor Nickel, Harald Walach, I. I. Session

Takashi Matsuoka

Siping Liu

From Linden-Popescu-Schlienz standard form and canonical form,the compact relative entropy of entanglement of 3-qubit pure state and the compact relative entropy of entanglement of W state are calculated.The fact that the compact relative entropy of entanglement is not invariant under LU transformation is pointed out,and the relation between the compact relative entropy of entanglement and the relative entropy of entanglement of Partovi is discussed.