Tighter monogamy and polygamy relations using Rényi-$\alpha$ entropy

Abstract

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

8 pages, 2 figures. Some typoes are corrected. arXiv admin note: substantial text overlap with arXiv:1703.02858 by other authors