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Advanced Quantum Technologies

Quantum State Ordering Driven by Quantum Battery Capacity and Correlation

Guoji Bai, Helin Gong, Bo Li, Laizhen Luo

Published Aug 7, 2025• 2 citations
Publisher

Abstract

Abstract The rapid advancements in quantum information science and quantum thermodynamics have led to increasingly interdisciplinary innovations. One notable development is the concept of the ergotropic gap, defined as the difference between global and local ergotropy. Building on this foundation, multipartite ergotropic gap indicators have been proposed to enhance methods of entanglement classification [Phys. Rev. A 109 , 062427 (2024)]. Motivated by this perspective, the thermodynamic notion of quantum battery capacity—closely related to ergotropy and defined as the energy difference between maximally and minimally achievable states under unitary evolution—is examined to address state ordering problems. The investigation focuses on comparing state orderings using three measures: battery capacity, entanglement of formation, and quantum discord, with particular emphasis on two‐qubit Bell‐diagonal states. Remarkably, certain classes of these states exhibit identical ordering patterns across all three measures under specific conditions.

DOI
10.1002/qute.202500303

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Abstract The rapid advancements in quantum information science and quantum thermodynamics have led to increasingly interdisciplinary innovations. One notable development is the concept of the ergotropic gap, defined as the difference between global and local ergotropy. Building on this foundation, multipartite ergotropic gap indicators have been proposed to enhance methods of entanglement classification [Phys. Rev. A 109 , 062427 (2024)]. Motivated by this perspective, the thermodynamic notion of quantum battery capacity—closely related to ergotropy and defined as the energy difference between maximally and minimally achievable states under unitary evolution—is examined to address state ordering problems. The investigation focuses on comparing state orderings using three measures: battery capacity, entanglement of formation, and quantum discord, with particular emphasis on two‐qubit Bell‐diagonal states. Remarkably, certain classes of these states exhibit identical ordering patterns across all three measures under specific conditions.
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.
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 The distribution relationship of quantum battery capacity is investigated. First, it is proved that for two‐qubit ‐states, the sum of the subsystem battery capacities does not exceed the total system's battery capacity, and the conditions are provided under which they are equal. Then define the difference between the total system's and subsystems' battery capacities as the residual battery capacity () and show that this can be divided into coherent and incoherent components. Furthermore, it is observed that this capacity monogamy relation for quantum batteries extends to general ‐qubit states and any ‐qubit state's battery capacity distribution can be optimized to achieve capacity gain through an appropriate global unitary evolution. Specifically, for general three‐qubit states, stronger distributive relations are derived for battery capacity. Quantum batteries are believed to hold significant potential for outperforming classical counterparts in the future. These findings contribute to the development and enhancement of quantum battery theory.
The quantum battery capacity is introduced in this Letter as a figure of merit that expresses the potential of a quantum system to store and supply energy. It is defined as the difference between the highest and the lowest energy that can be reached by means of the unitary evolution of the system. This function is closely connected to the ergotropy, but it does not depend on the temporary level of energy of the system. The capacity of a quantum battery can be directly linked with the entropy of the battery state, as well as with measures of coherence and 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.
Ergotropic-gap relations provide thermodynamic witnesses of quantum correlations, but a direct dynamical connection between extractable work and entanglement remains largely unexplored in multipartite non-Gaussian bosonic systems. Here, we establish such a connection for a bosonic quantum battery driven by a coherent-state superposition. Despite the infinite-dimensional Hilbert space, the dynamics retains a simple structure that allows the relevant work and correlation measures to be obtained exactly. We show that the loss of extractable work associated with the passive part of the battery energy is directly determined by charger-battery entanglement. This relation also separates the charging power into contributions from energy transfer and from changes in the battery spectrum. At the same time, multipartite correlations are progressively redistributed from charger-involving correlations to correlations internal to the battery. For a symmetric resonant protocol, complete energy transfer coincides with charger-battery disentanglement and fully extractable stored energy, while multipartite correlations within the battery are maximal. Individual cells, however, remain mixed, revealing a distinction between global and local work extraction. We further show that, in the regime considered, locally extractable work is entirely supported by energetic coherence. Under single-photon loss, the analytical structure survives, but environmental correlations separate charger disentanglement from maximal work extraction.