The presence of quantum multipartite entanglement implies the existence of a thermodynamic quantity known as the ergotropic gap, which is defined as the difference between the maximal global and local extractable works from the system. We establish a direct relation between the geometric measure of entanglement and the ergotropic gaps. We show that all the marginal ergotropic gaps form a convex polytope for each class of quantum states that are equivalent under stochastic local operations and classical communication (SLOCC). We finally introduce the concept of multipartite ergotropic gap indicators and use them to present a refined criterion for classifying entanglement under SLOCC.
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 have no extracted energy under any cyclic unitary process. In this paper, the focus is on the concept of marginal passive state energy and derive polygon inequalities for multi‐qubit entangled pure states. It is shown that the marginal passive state energies collectively form a convex polytope for each class of quantum states that are equivalent under SLOCC. Multipartite passive state energy criteria is introduced to classify multipartite entanglement under SLOCC. The present result provides a thermodynamic method to witness multipartite entanglement.
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 Letter, 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.
We develop a thermodynamic characterization of multimode entanglement in pure continuous-variable systems by quantifying the gap between globally and locally extractable work (ergotropy). For arbitrary pure multimode Gaussian states, we prove that the
2-local ergotropic gap is a faithful entanglement monotone across any bipartition and constitutes a functionally independent upper bound to the Renyi-2 entanglement entropy. We further introduce the
k-ergotropic score, the minimum
k-local ergotropic gap, and show that it faithfully quantifies multimode entanglement across
k partitions. For pure three-mode Gaussian states, we derive its closed-form relation with the geometric measure for genuine multimode entanglement
(k=2), and total Gaussian multimode entanglement
(k=3). For systems with more than three modes, the
k-ergotropic score becomes a functionally independent measure of multimode entanglement to the standard geometric measures. Our results reveal a direct operational hierarchy linking Gaussian multimode entanglement to work extraction under locality constraints, and provide a computable and experimentally accessible thermodynamic framework for characterizing quantum correlations.
Abstract Witness operators are a central tool to detect entanglement or to distinguish among the different entanglement classes of multiparticle systems, which can be defined using stochastic local operations and classical communication (SLOCC). We show a one-to-one correspondence between general SLOCC witnesses and a class of entanglement witnesses in an extended Hilbert space. This relation can be used to derive SLOCC witnesses from criteria for full separability of quantum states; moreover, given SLOCC witnesses can be viewed as entanglement witnesses. As applications of this relation we discuss the calculation of overlaps between different SLOCC classes and the SLOCC classification in -dimensional systems.
Extracting work from quantum system is one of the important areas in quantum thermodynamics. As a significant thermodynamic quantity, the ergotropy gap characterizes the difference between the global and local maximum extractable works. We derive an analytical upper bound of the ergotropic gap with respect to [Formula: see text] tripartite separable states. This bound also provides a necessary criterion for the separability of tripartite states. Detailed examples are presented to illustrate the efficiency of this separability criterion.