Ergotropic characterization of continuous variable entanglement

TL;DR

This paper introduces an entropy-free, thermodynamics-based criterion for detecting entanglement in continuous-variable Gaussian states using ergotropy, linking quantum correlations to energy extraction capabilities.

Contribution

It presents a novel ergotropic gap measure for entanglement detection that is both necessary and sufficient for a broad class of states, extending beyond entropy-based methods.

Findings

The ergotropic gap effectively distinguishes entangled from separable states.

The criterion applies to Gaussian states and some non-Gaussian states.

It provides an operational, energy-based method for entanglement detection.

Abstract

Continuous-variable quantum thermodynamics in the Gaussian regime provides a promising framework for investigating the energetic role of quantum correlations, particularly in optical systems. In this work, we introduce an entropy-free criterion for entanglement detection in bipartite Gaussian states, rooted in a distinct thermodynamic quantity: ergotropy--the maximum extractable work via unitary operations. By defining the relative ergotropic gap, which quantifies the disparity between global and local ergotropy, we derive two independent analytical bounds that distinguish entangled from separable states. These bounds coincide for a broad class of quantum states, making the criterion both necessary and sufficient in such cases. Unlike entropy-based measures, our ergotropic approach captures fundamentally different aspects of quantum correlations and entanglement, particularly in mixed continuous-variable systems. We also extend our analysis beyond the Gaussian regime to certain non-Gaussian states and observe that Gaussian ergotropy continues to reflect thermodynamic signatures in entangled states, albeit with some limitations. These findings establish a direct operational link between entanglement and energy storage, offering an experimentally accessible approach to entanglement detection in continuous-variable optical platforms.