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arxiv: 2510.25549 · v1 · submitted 2025-10-29 · 🪐 quant-ph

Charge-Preserving Operations in Quantum Batteries

Andr\'e H. A. Malavazi , Borhan Ahmadi , Pawe{\l} Horodecki , Pedro R. Dieguez This is my paper

Pith reviewed 2026-05-18 03:40 UTC · model grok-4.3

classification 🪐 quant-ph
keywords ergotropyquantum batteriesisoergotropic statesergotropy-preserving operationsquantum thermodynamicsGaussian statescharge preservation
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The pith

Ergotropy can be internally reorganized in quantum systems without changing its total value.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper defines isoergotropic states as quantum states sharing the same total ergotropy but differing in how that ergotropy is distributed among components. It also defines operations that move between these states while keeping the total fixed. The authors show this redistribution for qubit systems between coherent and incoherent parts and for Gaussian states between displacement and squeezing. They demonstrate that beam-splitter couplings to an auxiliary mode can enact these operations and track the accompanying energy and entropy changes. The work points to uses in designing better charging sequences for quantum batteries and in limiting unwanted charge loss when the battery interacts with its environment.

Core claim

The central claim is that ergotropy-preserving operations exist which transform the state of a quantum battery by redistributing its ergotropy between different physical contributions, such as coherence versus population inversion in two-level systems or displacement versus squeezing in Gaussian modes, without any net change in the total extractable work. These operations are accompanied by specific changes in the system's energy and entropy and can be realized using linear optical interactions with an auxiliary system.

What carries the argument

Isoergotropic states and the ergotropy-preserving operations that connect them, which alter the balance between coherent and incoherent ergotropy or between displacement and squeezing contributions while the sum remains constant.

If this is right

  • Redistribution of ergotropy between coherence and population inversion occurs in two-level systems with no loss in total value.
  • Redistribution between displacement and squeezing occurs in single-mode Gaussian states with no loss in total value.
  • Energy and entropy of the system vary in a controlled manner during the transformation.
  • Beam-splitter interactions with an auxiliary system provide a physical implementation that preserves total ergotropy.
  • These transformations support optimized charging protocols and help mitigate charge loss in open quantum batteries.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar preservation properties might hold for other measures of quantum resources beyond ergotropy.
  • Integrating these operations into charging cycles could improve the efficiency of quantum energy storage devices.
  • Extensions to multi-partite or higher-dimensional systems could uncover new ways to manage extractable work in complex quantum networks.

Load-bearing premise

The operations can be implemented using beam-splitter interactions with an auxiliary system without altering the overall extractable work.

What would settle it

A calculation or measurement demonstrating that the total ergotropy changes after applying a beam-splitter interaction to a quantum battery state, or that the component redistribution does not match the predicted isoergotropic mapping, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2510.25549 by Andr\'e H. A. Malavazi, Borhan Ahmadi, Pawe{\l} Horodecki, Pedro R. Dieguez.

Figure 1
Figure 1. Figure 1: FIG. 1: Isoergotropic states for (a) a single two-level [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) Isoergotropic surfaces at the Bloch sphere for distinct values of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) Ratio [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Isoergotropic operations. The continuous and [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Top: Bloch sphere representation of the (a) bat [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (a) Charge and (b) von Neumann entropy dy [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Ergotropy profile as a function of [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: (a) Ergotropy profile. The isoergotropic surfaces [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: (a) shows this behavior on L5 as a function of N and ξ; the green dashed curve marks the zero set of fµ¯(ξ, N). We quantify mixedness by the Rényi-2 entropy S2(ρ) = (1 − 2)−1 ln Tr[ρ 2 ] [91], for which S2 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Isoergotropic Gaussian operations. The con [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: (a) Charge and (b) Rényi-2 entropy dynamics [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Top: Parameter space representation of the [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Isoergotropic surfaces and optimal-power charg [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Ergotropy decay for (a)-(d) TLS (e)-(h) single-mode Gaussian-based open quantum batteries. (a) Ergotropy [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗
read the original abstract

Ergotropy provides a fundamental measure of the extractable work from a quantum system and, consequently, of the maximal useful energy, or charge, stored within it. Understanding how this quantity can be manipulated and transformed efficiently is crucial for advancing quantum energy management technologies. Here, we introduce and formalize the concepts of isoergotropic states and ergotropy-preserving operations, which reorganize the internal structure of ergotropy while keeping its total value unchanged. These ideas are illustrated for both discrete (two-level systems) and continuous-variable systems (single-mode Gaussian states). In each case, we show how ergotropy-preserving operations redistribute the respective coherent-incoherent and displacement-squeezing components. We further examine the thermodynamic exchanges accompanying ergotropy-preserving operations, including variations in energy and entropy, and demonstrate that these transformations can be dynamically implemented through standard beam-splitter-type interactions with an auxiliary system. Finally, we discuss the practical implications of isoergotropic states and operations in optimizing charging protocols and mitigating charge loss in open quantum batteries.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces and formalizes the concepts of isoergotropic states and ergotropy-preserving operations, which reorganize the internal structure of ergotropy (coherent-incoherent components for two-level systems and displacement-squeezing components for single-mode Gaussian states) while keeping its total value unchanged. These are illustrated on discrete and continuous-variable systems, with analysis of accompanying thermodynamic exchanges in energy and entropy. The work further claims that such operations can be dynamically implemented via standard beam-splitter-type interactions with an auxiliary system and discusses implications for optimizing charging protocols and mitigating charge loss in open quantum batteries.

Significance. If the claims hold, particularly the general dynamical realizability, the introduction of isoergotropic states and ergotropy-preserving operations could provide a useful framework for manipulating ergotropy structure without loss in quantum batteries. The illustrations on TLS and Gaussian states, combined with thermodynamic analysis, offer concrete examples that may aid protocol design in quantum thermodynamics.

major comments (1)
  1. [Abstract and dynamical implementation discussion] Abstract and dynamical implementation discussion: The claim that ergotropy-preserving operations can be dynamically realized through standard beam-splitter-type interactions with an auxiliary system while preserving total ergotropy is load-bearing for the open-system implications. Preservation requires that any change in Tr(Hρ) is exactly offset by a change in Tr(Hρ_passive). This offset holds automatically only for particular auxiliary states (e.g., vacuum for displacement redistribution); for generic thermal or squeezed auxiliaries the spectrum of the reduced battery state shifts in a way that alters ergotropy. The manuscript should explicitly state the required conditions on the auxiliary and verify them beyond the specific TLS and Gaussian illustrations.
minor comments (2)
  1. [Definitions section] The formal definitions of isoergotropic states and ergotropy-preserving operations would benefit from explicit mathematical expressions presented early in the text to improve accessibility.
  2. [Illustrations and figures] Any figures showing redistribution of coherent/incoherent or displacement/squeezing components should include clear labels distinguishing the reorganized parts from the total ergotropy.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the single major comment below, agreeing where appropriate and outlining the revisions that will be made.

read point-by-point responses

  1. Referee: Abstract and dynamical implementation discussion: The claim that ergotropy-preserving operations can be dynamically realized through standard beam-splitter-type interactions with an auxiliary system while preserving total ergotropy is load-bearing for the open-system implications. Preservation requires that any change in Tr(Hρ) is exactly offset by a change in Tr(Hρ_passive). This offset holds automatically only for particular auxiliary states (e.g., vacuum for displacement redistribution); for generic thermal or squeezed auxiliaries the spectrum of the reduced battery state shifts in a way that alters ergotropy. The manuscript should explicitly state the required conditions on the auxiliary and verify them beyond the specific TLS and Gaussian illustrations.

    Authors: We agree with the referee that the dynamical realizability claim requires careful qualification, as ergotropy preservation under beam-splitter interactions is not automatic for arbitrary auxiliary states. In the current manuscript the explicit constructions and numerical illustrations are restricted to auxiliary states (vacuum for the Gaussian case and the appropriate ground-state equivalent for the TLS case) for which the required offset between ΔTr(Hρ) and ΔTr(Hρ_passive) holds exactly, so that only the internal coherent/incoherent or displacement/squeezing decomposition is redistributed. We will revise the relevant sections (including the abstract and the dynamical-implementation discussion) to state these conditions explicitly: the auxiliary must be prepared in a state whose spectrum, after the unitary interaction, ensures that any energy change in the battery is precisely compensated by a change in its passive energy. We will also add a short general argument showing why the vacuum (or ground) choice satisfies the condition and note that generic thermal or squeezed auxiliaries generally violate it, thereby limiting the open-system implications to the auxiliary states we have verified. These changes will be incorporated in the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper defines isoergotropic states and ergotropy-preserving operations directly from the established ergotropy functional (energy minus passive energy), then illustrates redistribution of coherent/incoherent or displacement/squeezing components on TLS and Gaussian states. Dynamical realization is asserted via explicit beam-splitter unitaries with an auxiliary mode. No quoted step reduces a claimed prediction or uniqueness result to a fitted parameter, self-definition, or load-bearing self-citation chain; the constructions remain independent of the target claims and rely on standard quantum-optical interactions rather than tautological renaming or imported ansätze.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The contribution rests on standard quantum mechanics for discrete and continuous-variable systems plus the pre-existing definition of ergotropy; the new states and operations are introduced by definition rather than derived from more fundamental principles.

axioms (1)
  • standard math Standard quantum mechanics and thermodynamics apply to the description of ergotropy in two-level and Gaussian states.
    The paper builds directly on the established definition of ergotropy without introducing new physical laws.
invented entities (2)
  • isoergotropic states no independent evidence
    purpose: States in which the internal distribution of ergotropy can be reorganized while the total remains fixed.
    Newly defined concept whose independent experimental signature is not provided in the abstract.
  • ergotropy-preserving operations no independent evidence
    purpose: Operations that perform the reorganization of ergotropy components.
    Newly introduced class of operations whose concrete realization is only sketched via beam-splitter interactions.

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Reference graph

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