Multipartite entanglement measures based on the thermodynamic framework

TL;DR

This paper introduces a thermodynamics-based framework for measuring multipartite entanglement, proposing a new entanglement measure called ergotropic-gap concentratable entanglement that effectively distinguishes different quantum states.

Contribution

It develops a unified thermodynamic approach to quantify multipartite entanglement and introduces a novel measure with desirable properties, applicable to various quantum states.

Findings

The new measure satisfies key entanglement properties.

It distinguishes GHZ and W states effectively.

It detects entanglement in four-partite star networks.

Abstract

In this work, we introduce a unified method to characterize and measure multipartite entanglement using the framework of thermodynamics. A family of the new entanglement measures is proposed: \textit{ergotropic-gap concentratable entanglement}. Furthermore, we establish that ergotropic-gap concentratable entanglement constitutes a well-defined entanglement measure within a specific parameter regime, satisfying key properties including continuity, majorization monotonicity and monogamy. We demonstrate the utility of this measure by showing it effectively distinguishes between multi-qubit Greenberger-Horne-Zeilinger states and W states. It also proves effective in detecting entanglement in specific classes of four-partite star quantum network states.