# Detecting Gaussian entanglement via extractable work

## TL;DR

This paper demonstrates that the amount of work extractable from a bipartite Gaussian state in a Szilard-like engine can serve as a practical witness for entanglement, linking quantum thermodynamics with quantum information.

## Contribution

It introduces a novel method to detect Gaussian entanglement through work extraction, providing a quantitative criterion and extending the approach to tripartite states.

## Key findings

- Extractable work can witness bipartite entanglement in Gaussian states.
- The protocol is necessary and sufficient for squeezed thermal states.
- Full inseparability classes cannot be distinguished solely by work extraction.

## Abstract

We show how the presence of entanglement in a bipartite Gaussian state can be detected by the amount of work extracted by a continuos variable Szilard-like device, where the bipartite state serves as the working medium of the engine. We provide an expression for the work extracted in such a process and specialize it to the case of Gaussian states. The extractable work provides a sufficient condition to witness entanglement in generic two-mode states, becoming also necessary for squeezed thermal states. We extend the protocol to tripartite Gaussian states, and show that the full structure of inseparability classes cannot be discriminated based on the extractable work. This suggests that bipartite entanglement is the fundamental resource underpinning work extraction.