# Bound on Ergotropic Gap for Bipartite Separable States

## TL;DR

This paper establishes a bound on the ergotropic gap for bipartite separable states, providing a tool to detect entanglement and understand correlations' role in quantum thermodynamics.

## Contribution

It derives a new bound on the ergotropic gap for bipartite separable states, linking it to entanglement detection and operational criteria in quantum thermodynamics.

## Key findings

- Violation of the bound certifies entanglement.
- The ergotropic gap is a monotone under LOCC for pure states.
- The criterion can witness the dimension of bipartite states.

## Abstract

Presence of correlations among the constituent quantum systems has a great relevance in thermodynamics. Significant efforts have been devoted to investigate the role of correlations in work extraction, among others. Here, we derive a bound on the difference between global and local extractable work by unitary operations (ergotropic gap), for bipartite separable states. Violation of this bound necessarily certifies the presence of entanglement. This gap is shown to be a monotone under LOCC assisted state transformations for pure bipartite quantum states. Our criterion has an implication in witnessing the dimension of a bipartite quantum state, with same local dimensions. On the other hand, our result gives an operational meaning to the Nielsen-Kempe disorder criterion. We also propose a schematic model to realize the separability bound experimentally and to detect entanglement for a restricted class of quantum states.