Witnessing entanglement in hybrid systems

TL;DR

This paper generalizes entanglement witnesses to systems with quantized positions, enabling entanglement detection in hybrid quantum systems and analyzing how additional degrees of freedom influence measurement outcomes.

Contribution

It introduces a new class of entanglement witnesses accounting for quantized positions, specifically applied to trapped ion chains, enhancing entanglement detection methods in hybrid systems.

Findings

Quantized positions affect entanglement measurement statistics.

Vibronic states can act as an environment impacting entanglement detection.

The method enables detection of hybrid entanglement in specific cases.

Abstract

We extend the definition of entanglement witnesses based on structure factors to the case in which the position of the scatterers is quantized. This allows us to study entanglement detection in hybrid systems. We provide several examples that show how these extra degrees of freedom affect the detection of entanglement by directly contributing to the measurement statistics. We specialize the proposed witness operators for a chain of trapped ions. Within this framework, we show how the collective vibronic state of the chain can act as an undesired quantum environment and how ions quantum motion can affect the entanglement detection. Finally, we investigate some specific cases where the method proposed leads to detection of hybrid entanglement.