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  • Open Access

Correlation enhanced autonomous quantum battery charging via structured reservoirs

A. Khoudiri1,2,*, A. El Allati1,†, Y. Khlifi1,3, K. El Anouz1,‡, and Ö. E. Müstecaplıoğlu4,5,§

  • *Contact author: khoudiri.achraf@etu.uae.ac.ma
  • †Contact author: eabderrahim@uae.ac.ma
  • ‡Contact author: kelanouz@uae.ac.ma
  • §Contact author: omustecap@ku.edu.tr
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Phys. Rev. E 114, 034116 – Published 10 September, 2026

DOI: https://doi.org/10.1103/x2s1-27k1

Abstract

In this work, we investigate the autonomous charging process of a quantum battery coupled to a structured reservoir composed of two qubits, each locally coupled to its own bosonic thermal bath. Moreover, the reservoir interacts with a charger–battery architecture through three configurations: (I) direct coupling between reservoir qubits and battery; (II) collective coupling among the reservoir qubits, charger, and battery; and (III) a collective coupling between the reservoir qubits and charger together with a local charger–battery interaction. However, by using incoherent and coherent initial states, we analyze the stored energy, ergotropy, and charging power of the battery, and derive upper and lower bounds on the extractable work in terms of the free energy of coherence and the correlations exchanged between subsystems. Our results show that global and local coherences, as well as total correlations, act as quantum resources that enhance autonomous charging. Additionally, we demonstrate that the free energy stored in the quantum battery splits into contributions from coherence and correlations, providing numerical evidence that supports the derived ergotropy bounds. Importantly, this work highlights how structured reservoirs enable autonomous and resource-enhanced quantum battery operation.

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References (63)

  1. M. F. Riedel, D. Binosi, R. Thew, and T. Calarco, The European quantum technologies flagship programme, Quantum Sci. Technol. 2, 030501 (2017).
  2. A. Acín, I. Bloch, H. Buhrman, T. Calarco, et al., The quantum technologies roadmap: A European community view, New J. Phys. 20, 080201 (2018).
  3. J. Q. Quach, G. Cerullo, and T. Virgili, Quantum batteries: The future of energy storage? Joule 7, 2195 (2023).
  4. A. Demir, E. Yildiz, and C. Kaya, Application of quantum computing in the design of new materials for batteries, J. Tecnol. Quantica 1, 288 (2024).
  5. D. Farina, G. M. Andolina, A. Mari, M. Polini, and V. Giovannetti, Charger-mediated energy transfer for quantum batteries: An open-system approach, Phys. Rev. B 99, 035421 (2019).
  6. G. M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giovannetti, and M. Polini, Charger-mediated energy transfer in exactly solvable models for quantum batteries, Phys. Rev. B 98, 205423 (2018).
  7. C.-J. Wang and F.-Q. Dou, Ergotropy in quantum batteries, Chin. Phys. Lett. 43, 060602 (2026).
  8. S. Elghaayda, A. Ali, S. Al-Kuwari, A. Czerwinski, M. Mansour, and S. Haddadi, Performance of a superconducting quantum battery, Adv. Quantum Technol. 8, 2400651 (2025).
  9. F.-M. Yang and F.-Q. Dou, Resonator-qutrit quantum battery, Phys. Rev. A 109, 062432 (2024).
  10. F.-Q. Dou and F.-M. Yang, Superconducting transmon qubit-resonator quantum battery, Phys. Rev. A 107, 023725 (2023).
  11. Z. G. Lu, G. Tian, X. Y. Lü, and C. Shang, Topological quantum batteries, Phys. Rev. Lett. 134, 180401 (2025).
  12. B. Ahmadi, P. Mazurek, S. Barzanjeh, and P. Horodecki, Super-optimal charging of quantum batteries via reservoir engineering, Phys. Rev. Appl. 23, 024010 (2025).
  13. H.-L. Shi, S. Ding, Q.-K. Wan, X.-H. Wang, and W.-L. Yang, Entanglement, coherence, and extractable work in quantum batteries, Phys. Rev. Lett. 129, 130602 (2022).
  14. F. Cavaliere, G. Gemme, G. Benenti, D. Ferraro, and M. Sassetti, Dynamical blockade of a reservoir for optimal performances of a quantum battery, Commun. Phys. 8, 76 (2025).
  15. A. Khoudiri, A. Ullah, A. El Allati, and Ö. E. Müstecaplolu, Collective-dissipation-induced dark and metastable-like states for enhanced quantum battery performance, arXiv:2608.09693.
  16. Y. Yao and X. Q. Shao, Reservoir-assisted quantum battery charging at finite temperatures, Phys. Rev. A 111, 062616 (2025).
  17. B. Ahmadi, P. Mazurek, P. Horodecki, and S. Barzanjeh, Nonreciprocal quantum batteries, Phys. Rev. Lett. 132, 210402 (2024).
  18. K. Xu, H. J. Zhu, G. F. Zhang, and W. M. Liu, Enhancing the performance of an open quantum battery via environment engineering, Phys. Rev. E 104, 064143 (2021).
  19. J. L. Li, H. Z. Shen, and X. X. Yi, Quantum batteries in non-Markovian reservoirs, Opt. Lett. 47, 5614 (2022).
  20. W.-L. Song, J.-L. Wang, B. Zhou, W.-L. Yang, and J.-H. An, Self-discharging mitigated quantum battery, Phys. Rev. Lett. 135, 020405 (2025).
  21. T. M. Mendonça, A. M. Souza, R. J. de Assis, N. G. de Almeida, R. S. Sarthour, I. S. Oliveira, and C. J. Villas-Boas, Reservoir engineering for maximally efficient quantum engines, Phys. Rev. Res. 2, 043419 (2020).
  22. J. Yang, S. Fang, C. Zhao, C. Shan, and B. Xiong, Quantum battery via reservoir engineering, Phys. Rev. Appl. 25, 034013 (2026).
  23. F. T. Tabesh, F. H. Kamin, and S. Salimi, Environment-mediated charging process of quantum batteries, Phys. Rev. A 102, 052223 (2020).
  24. M. L. Hu, T. Gao, and H. Fan, Efficient wireless charging of a quantum battery, Phys. Rev. A 111, 042216 (2025).
  25. M.-L. Song, L.-J. Li, X.-K. Song, L. Ye, and D. Wang, Environment-mediated entropic uncertainty in charging quantum batteries, Phys. Rev. E 106, 054107 (2022).
  26. F. Barra, Dissipative charging of a quantum battery, Phys. Rev. Lett. 122, 210601 (2019).
  27. M. Alimuddin, T. Guha, and P. Parashar, Structure of passive states and its implication in charging quantum batteries, Phys. Rev. E 102, 022106 (2020).
  28. G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchison, J. Goold, and F. Plastina, Quantum coherence and ergotropy, Phys. Rev. Lett. 125, 180603 (2020).
  29. A. Touil, B. Çakmak, and S. Deffner, Ergotropy from quantum and classical correlations, J. Phys. A: Math. Theor. 55, 025301 (2022).
  30. T. Biswas, M. Łobejko, P. Mazurek, K. Jałowiecki, and M. Horodecki, Extraction of ergotropy: Free energy bound and application to open cycle engines, Quantum 6, 841 (2022).
  31. R. Castellano, D. Farina, V. Giovannetti, and A. Acin, Extended local ergotropy, Phys. Rev. Lett. 133, 150402 (2024).
  32. G. G. Damas, R. J. de Assis, and N. G. de Almeida, Cooling with fermionic thermal reservoirs, Phys. Rev. E 107, 034128 (2023).
  33. G. Manzano, Squeezed thermal reservoir as a generalized equilibrium reservoir, Phys. Rev. E 98, 042123 (2018).
  34. S. Lorenzo, F. Ciccarello, and G. M. Palma, Composite quantum collision models, Phys. Rev. A 96, 032107 (2017).
  35. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
  36. A. Rivas Vargas, Open quantum systems and quantum information dynamics, Doctoral thesis, Universitaire Ulm, 2011.
  37. C. Fleming, N. I. Cummings, C. Anastopoulos, and B. L. Hu, The rotating-wave approximation: Consistency and applicability from an open quantum system analysis, J. Phys. A: Math. Theor. 43, 405304 (2010).
  38. S. Ghosh, A. Opala, M. Matuszewski, T. Paterek, and T. C. H. Liew, Quantum reservoir processing, npj Quantum Inf. 5, 35 (2019).
  39. B. L. Fang, J. Shi, and T. Wu, Quantum-memory-assisted entropic uncertainty relation and quantum coherence in structured reservoir, Int. J. Theor. Phys. 59, 763 (2020).
  40. A. Oularabi, A. El Allati, and K. El Anouz, Enhancing ergotropy of quantum batteries through coherence and non-Markovianity, Physica A 679, 131003 (2025).
  41. Y. Aiache, A. Ullah, Ö. E. Müstecaplıoğlu, and A. E. Allati, Quantum metrology of a structured reservoir, Phys. Rev. A 111, 062619 (2025).
  42. N. Linden, S. Popescu, and P. Skrzypczyk, How small can thermal machines be? The smallest possible refrigerator, Phys. Rev. Lett. 105, 130401 (2010).
  43. A. Khoudiri, A. El Allati, Ö. E. Müstecaplıoğlu, and K. El Anouz, Non-Markovianity and a generalized Landauer bound for a minimal quantum autonomous thermal machine with a work qubit, Phys. Rev. E 111, 044124 (2025).
  44. D. C. McKay, S. Filipp, A. Mezzacapo, E. Magesan, J. M. Chow, and J. M. Gambetta, Universal gate for fixed-frequency qubits via a tunable bus, Phys. Rev. Appl. 6, 064007 (2016).
  45. A. P. Place, L. V. Rodgers, P. Mundada, B. M. Smitham, M. Fitzpatrick, Z. Leng, et al., New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds, Nat. Commun. 12, 1779 (2021).
  46. A. Khoudiri, K. El Anouz, and A. El Allati, Quantum entanglement generation in autonomous thermal machines: Effects of non-Markovianity, Hilbert space structure, and quantum coherence, AVS Quantum Sci. 8, 022001 (2026).
  47. M. Müller, K. Hammerer, Y. L. Zhou, C. F. Roos, and P. Zoller, Simulating open quantum systems: From many-body interactions to stabilizer pumping, New J. Phys. 13, 085007 (2011).
  48. C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, Coupling effects in single-mode and multimode resonator-coupled system, Opt. Express 27, 17718 (2019).
  49. J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, et al., Coupling superconducting qubits via a cavity bus, Nature (London) 449, 443 (2007).
  50. W. De Roeck and C. Maes, Quantum version of free-energy–irreversible-work relations, Phys. Rev. E 69, 026115 (2004).
  51. M. Lostaglio, D. Jennings, and T. Rudolph, Description of quantum coherence in thermodynamic processes requires constraints beyond free energy, Nat. Commun. 6, 6383 (2015).
  52. E. Chitambar and G. Gour, Comparison of incoherent operations and measures of coherence, Phys. Rev. A 94, 052336 (2016).
  53. T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113, 140401 (2014).
  54. J. P. Santos, L. C. Céleri, G. T. Landi, and M. Paternostro, The role of quantum coherence in non-equilibrium entropy production, npj Quantum Inf. 5, 23 (2019).
  55. D. Šafránek, D. Rosa, and F. C. Binder, Work extraction from unknown quantum sources, Phys. Rev. Lett. 130, 210401 (2023).
  56. P. Skrzypczyk, R. Silva, and N. Brunner, Passivity, complete passivity, and virtual temperatures, Phys. Rev. E 91, 052133 (2015).
  57. G. L. Giorgi and S. Campbell, Multipartite quantum and classical correlations in symmetric n-qubit mixed states, Quantum Inf. Process. 15, 4599 (2016).
  58. D. Murphy, A. Kiely, I. D'Amico, and S. Campbell, Ergotropy transport in a one-dimensional spin chain, Phys. Rev. A 112, 052214 (2025).
  59. M. J. Sarmah and H. P. Goswami, Noise-induced coherent ergotropy of a quantum heat engine, Phys. Rev. A 110, 032213 (2024).
  60. J.-Y. Gyhm and U. R. Fischer, Beneficial and detrimental entanglement for quantum battery charging, AVS Quantum Sci. 6, 012001 (2024).
  61. L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, et al., Demonstration of two-qubit algorithms with a superconducting quantum processor, Nature (London) 460, 240 (2009).
  62. S. Zakavati, F. T. Tabesh, and S. Salimi, Bounds on charging power of open quantum batteries, Phys. Rev. E 104, 054117 (2021).
  63. G. Francica, Quantum correlations and ergotropy, Phys. Rev. E 105, L052101 (2022).

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Phys. Rev. E 114, 034116– Published 10 September, 2026
  • Received 9 December 2025
  • Accepted 26 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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