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  • Open Access

Charge-Preserving Operations in Quantum Batteries

André H.A. Malavazi1,*, Borhan Ahmadi1,†, Paweł Horodecki1, and Pedro R. Dieguez2,1,‡

  • *Contact author: andrehamalavazi@gmail.com
  • †Contact author: borhan.ahmadi@ug.edu.pl
  • ‡Contact author: dieguez.pr@gmail.com
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PRX Energy 5, 023004 – Published 28 April, 2026

DOI: https://doi.org/10.1103/2jtp-jpkn

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.

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Popular Summary

Ergotropy measures how much useful energy, or charge, can be extracted from a quantum system. Efficiently controlling this energy is crucial for advancing technologies like quantum batteries. In this work, the authors present a way to reorganize the internal structure of ergotropy without changing its total amount, through what they call isoergotropic states and ergotropy-preserving operations. These ideas provide new tools for improving charging protocols in quantum batteries and preventing energy loss to the environment. In simple terms, they show how to convert the energy inside a quantum battery while keeping the total charge fixed. This brings us a step closer to making quantum batteries more reliable and practical for future technologies.

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PRX Energy 5, 023004– Published 28 April, 2026
  • Received 3 November 2025
  • Revised 24 February 2026
  • Accepted 30 March 2026
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