Monogamy and polygamy for multi-qubit entanglement using Rényi entropy

Jeong San Kim, Barry C. Sanders

Published 2009-11-27Version 1

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 $0<\epsilon<0.01$.