Classifying multiparticle entanglement with passive state energies

TL;DR

This paper introduces a thermodynamic approach using passive state energies to classify and witness multipartite entanglement in multi-qubit systems, providing a novel criterion based on convex polytopes.

Contribution

It derives polygon inequalities for marginal passive state energies and establishes a thermodynamic criterion for classifying multipartite entanglement under SLOCC.

Findings

Marginal passive state energies form convex polytopes for SLOCC classes

Polygon inequalities serve as entanglement witnesses

Thermodynamic method classifies multipartite entanglement

Abstract

Thermodynamics as a fundamental branch of physics examines the relationships between heat, work, and energy. The maximum energy extraction can be characterized by using the passive states that has no extracted energy under any cyclic unitary process. In this paper, we focus on the concept of marginal passive state energy and derive polygon inequalities for multi-qubit entangled pure states. We show that the marginal passive state energies collectively form a convex polytope for each class of quantum states that are equivalent under SLOCC. We finally introduce multipartite passive state energy criteria to classify multipartite entanglement under SLOCC. The present result provides a thermodynamic method to witness multipartite entanglement.