Lower and upper bounds for entanglement of R\'enyi-$\alpha$ entropy

TL;DR

This paper derives analytical bounds for the entanglement Rénnyi-$$ entropy in bipartite quantum systems, enhancing understanding of this entanglement measure and its relation to other measures.

Contribution

It provides the first analytical lower and upper bounds for entanglement Rénnyi-$$ entropy in arbitrary dimensions and explores its connections with other entanglement measures.

Findings

Derived analytical bounds for entanglement Rénnyi-$$ entropy.

Applied bounds to specific quantum system examples.

Established relations between Rénnyi-$$ entropy and other entanglement measures.

Abstract

Entanglement R\'enyi-$\alpha$ entropy is an entanglement measure. It generalizes the entanglement of formation, and they coincide when $\alpha$ tends to 1. We derive analytical lower and upper bounds for the entanglement R\'enyi-$\alpha$ entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement R\'enyi-$\alpha$ entropy and some other entanglement measures.