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

TL;DR

This paper derives tighter monogamy and polygamy relations for quantum entanglement using Rényi-$\alpha$ entropy, applicable within specific parameter ranges, improving upon existing bounds in quantum information theory.

Contribution

It introduces new, tighter monogamy and polygamy relations for Rényi-$\alpha$ entanglement, expanding the understanding of quantum entanglement sharing constraints.

Findings

Derived new monogamy relations for Rényi-$\alpha$ entanglement.

Established tighter polygamy relations for Rényi-$\alpha$ entanglement of assistance.

Applicable within specific $\alpha$ and $\mu$ parameter ranges.

Abstract

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.