Detecting entanglement with non-hermitian operators

TL;DR

This paper develops new entanglement detection criteria using non-hermitian operators, applicable to various quantum systems, and demonstrates their effectiveness through examples like the Dicke model.

Contribution

The paper introduces strengthened entanglement conditions based on non-hermitian operators, invariant under local unitaries, expanding tools for detecting quantum entanglement.

Findings

Derived entanglement conditions for field-atom systems

Applied conditions to the Dicke model example

Showed invariance under local Gaussian operations

Abstract

We derive several entanglement conditions employing non-hermitian operators. We start with two conditions that were derived previously for field mode operators, and use them to derive conditions that can be used to show the existence of field-atom entanglement and entanglement between groups of atoms. The original conditions can be strengthened by making them invariant under certain sets of local unitary transformations, such as Gaussian operations. We then apply these conditions to several examples, such as the Dicke model. We conclude with a short discussion of how local uncertainty relations with non-hermitian operators can be used to derive entanglement conditions.