Tighter monogamy and polygamy relations using R\'{e}nyi-$\alpha$ entropy

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