Monogamy and polygamy for multi-qubit entanglement using R\'enyi entropy

TL;DR

This paper investigates the monogamy and polygamy properties of multi-qubit entanglement using Renyi entropy, establishing proofs for certain parameters and providing numerical evidence for others.

Contribution

It proves monogamy of multi-qubit entanglement for alpha geq 2 and conjectures polygamy inequalities with strong numerical support for a range of alpha.

Findings

Monogamy holds for alpha geq 2.

Numerical evidence supports polygamy conjecture for 0.83-epsilon leq alpha leq 1.43+epsilon.

Conjecture extends understanding of entanglement sharing in multi-qubit systems.

Abstract

Using R\'enyi-$\alpha$ entropy to quantify bipartite entanglement, we prove monogamy of entanglement in multi-qubit systems for $\alpha \geq 2$. We also conjecture a polygamy inequality of multi-qubit entanglement with strong numerical evidence for $0.83-\epsilon \leq \alpha \leq 1.43+\epsilon$ with $0<\epsilon<0.01$.