Relationship between the linear entropy, the von Neumann entropy and the atomic Wehrl entropy for the Jaynes-Cummings model

TL;DR

This paper explores the relationships among different entanglement measures in the Jaynes-Cummings model, deriving a closed form for the atomic Wehrl entropy and proposing the Bloch sphere radius as a more practical entanglement quantifier.

Contribution

It analytically derives a closed form for the atomic Wehrl entropy and advocates using the Bloch sphere radius over entropic measures for entanglement quantification in JCM.

Findings

Derived a closed form for atomic Wehrl entropy.

Established the Bloch sphere radius as a better entanglement measure.

Compared entropic measures and the Bloch sphere radius in JCM.

Abstract

The linear entropy, the von Neumann entropy and the atomic Wehrl entropy are frequently used to quantify entanglement in the quantum systems. These relations provide typical information on the entanglement in the Jaynes-Cummings model (JCM). In this Letter, we explain the origin of this analytically and derive a closed form for the atomic Wehrl entropy. Moreover, we show that it is more convenient to use the Bloch sphere radius for quantifying entanglement in the JCM instead of these entropic relations.