# Fundamental limitations to local energy extraction in quantum systems

## TL;DR

This paper characterizes when local energy extraction from entangled quantum systems is impossible, providing necessary and sufficient conditions, and extends previous results with quantitative bounds and applicability to thermodynamic limits.

## Contribution

It introduces semidefinite programming techniques to analyze passivity in quantum thermodynamics and strengthens existing bounds on temperature thresholds for energy extraction restrictions.

## Key findings

- Necessary and sufficient conditions for local energy extraction impossibility.
- Quantitative bound on the temperature threshold for passivity.
- No-go results applicable to thermal states in the thermodynamic limit.

## Abstract

We examine when it is possible to locally extract energy from a bipartite quantum system in the presence of strong coupling and entanglement, a task which is expected to be restricted by entanglement in the low-energy eigenstates. We fully characterize this distinct notion of "passivity" by finding necessary and sufficient conditions for such extraction to be impossible, using techniques from semidefinite programming. This is the first time in which such techniques are used in the context of energy extraction, which opens a way of exploring further kinds of passivity in quantum thermodynamics. We also significantly strengthen a previous result of Frey et al., by showing a physically relevant quantitative bound on the threshold temperature at which this passivity appears. Furthermore, we show how this no-go result also holds for thermal states in the thermodynamic limit, provided that the spatial correlations decay sufficiently fast, and we give numerical examples.