Tighter monogamy and polygamy relations using R\'{e}nyi-$\alpha$ entropy. (arXiv:1810.09131v2 [quant-ph] UPDATED)

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
$\alpha\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $\mu\geqslant2$, and polygamy
relations satisfied by the $\mu$-th power of R\'{e}nyi-$\alpha$ entanglement of
assistance with $\alpha\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $0\leq\mu\leq1$.
These relations are shown to be tighter than the existing ones.

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