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  • Open Access

Quantum advantage from negativity of work quasiprobability distributions

Gianluca Francica*

  • *Contact author: gianluca.francica@gmail.com
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APS Open Sci. 1, 000093 – Published 13 August, 2026Erratum APS Open Sci. 1, 000160 (2026)

DOI: https://doi.org/10.1103/xwk6-qzzw

Abstract

Quantum batteries can be charged by performing a work “instantaneously” in the limit of a large number of cells, achieving a so-called quantum advantage. In general, the work exhibits statistics that can be represented by a quasiprobability in the presence of initial quantum coherence in the energy basis. Here, we show that these two concepts of quantum thermodynamics, which apparently appear disconnected, can show a simple relation. Specifically, if a certain work distribution shows negativity asymptotically in the limit of a large number of cells and in a certain time interval, then we surely get a quantum advantage in the charging process. In particular, we prove this for a direct charging protocol performed with a class of charging Hamiltonian operators.

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Erratum

Erratum: Quantum advantage from negativity of work quasiprobability distributions [APS Open Sci. 1, 000093 (2026)]

Gianluca Francica
APS Open Sci. 1, 000160 (2026)

Article Text

References (57)

  1. F. Campaioli, F. A. Pollock, and S. Vinjanampathy, Quantum batteries, in Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, edited by F. Binder, L. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer, Cham, 2018), Vol. 195.
  2. S. Bhattacharjee and A. Dutta, Quantum thermal machines and batteries, Eur. Phys. J. B 94, 239 (2021).
  3. F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Colloquium: Quantum batteries, Rev. Mod. Phys. 96, 031001 (2024).
  4. R. Alicki and M. Fannes, Entanglement boost for extractable work from ensembles of quantum batteries, Phys. Rev. E 87, 042123 (2013).
  5. A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhys. Lett. 67, 565 (2004).
  6. G. Francica, J. Goold, F. Plastina, and M. Paternostro, Daemonic ergotropy: Enhanced work extraction from quantum correlations, npj Quantum Inf. 3, 12 (2017).
  7. F. Bernards, M. Kleinmann, O. Gühne, and M. Paternostro, Daemonic ergotropy: Generalised measurements and multipartite settings, Entropy 21, 771 (2019).
  8. A. Touil, B. Çakmak, and S. Deffner, Ergotropy from quantum and classical correlations, J. Phys. A: Math. Theor. 55, 025301 (2022).
  9. C. Cruz, M. F. Anka, M. S. Reis, R. Bachelard, and A. C. Santos, Quantum battery based on quantum discord at room temperature, Quantum Sci. Technol. 7, 025020 (2022).
  10. G. Francica, Quantum correlations and ergotropy, Phys. Rev. E 105, L052101 (2022).
  11. 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).
  12. B. Çakmak, Ergotropy from coherences in an open quantum system, Phys. Rev. E 102, 042111 (2020).
  13. Z. Niu, Y. Wu, Y. Wang, X. Rong, and J. Du, Experimental investigation of coherent ergotropy in a single spin system, Phys. Rev. Lett. 133, 180401 (2024).
  14. K. V. Hovhannisyan, M. Perarnau-Llobet, M. Huber, and A. Acin, Entanglement generation is not necessary for optimal work extraction, Phys. Rev. Lett. 111, 240401 (2013).
  15. G. Francica, Resource theories with completely passive states and passive states as free states, Phys. Rev. E 111, 014141 (2025).
  16. F. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Quantacell: Powerful charging of quantum batteries, New J. Phys. 17, 075015 (2015).
  17. F. Campaioli, F. A. Pollock, F. C. Binder, L. Céleri, J. Goold, S. Vinjanampathy, and K. Modi, Enhancing the charging power of quantum batteries, Phys. Rev. Lett. 118, 150601 (2017).
  18. J.-Y. Gyhm, D. Šafránek, and D. Rosa, Quantum charging advantage cannot be extensive without global operations, Phys. Rev. Lett. 128, 140501 (2022).
  19. S. Julia-Farre, T. Salamon, A. Riera, M. N. Bera, and M. Lewenstein, Bounds on the capacity and power of quantum batteries, Phys. Rev. Res. 2, 023113 (2020).
  20. D. Ferraro, M. Campisi, G. M. Andolina, V. Pellegrini, and M. Polini, High-power collective charging of a solid-state quantum battery, Phys. Rev. Lett. 120, 117702 (2018).
  21. G. M. Andolina, M. Keck, A. Mari, M. Campisi, V. Giovannetti, and M. Polini, Extractable work, the role of correlations, and asymptotic freedom in quantum batteries, Phys. Rev. Lett. 122, 047702 (2019).
  22. 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).
  23. D. Farina, G. M. Andolina, A. Mari, M. Polini, and V. Giovannetti, Charger-mediated energy transfer for quantum batteries, Phys. Rev. B 99, 035421 (2019).
  24. Y. Y. Zhang, T. R. Yang, L. Fu, and X. Wang, Powerful harmonic charging in a quantum battery, Phys. Rev. E 99, 052106 (2019).
  25. G. M. Andolina, M. Keck, A. Mari, V. Giovannetti, and M. Polini, Quantum versus classical many-body batteries, Phys. Rev. B 99, 205437 (2019).
  26. A. Crescente, M. Carrega, M. Sassetti, and D. Ferraro, Ultrafast charging in a two-photon Dicke quantum battery, Phys. Rev. B 102, 245407 (2020).
  27. D. Rossini, G. M. Andolina, and M. Polini, Many-body localized quantum batteries, Phys. Rev. B 100, 115142 (2019).
  28. D. Rossini, G. M. Andolina, D. Rosa, M. Carrega, and M. Polini, Quantum advantage in the charging process of Sachdev-Ye-Kitaev batteries, Phys. Rev. Lett. 125, 236402 (2020).
  29. D. Rosa, D. Rossini, G. M. Andolina, M. Polini, and M. Carrega, Ultra-stable charging of fast-scrambling SYK quantum batteries, J. High Energ. Phys. 11 (2020) 067.
  30. M. Carrega, J. Kim, and D. Rosa, Unveiling operator growth using spin correlation functions, Entropy 23, 587 (2021).
  31. J.-Y. Gyhm and U. R. Fischer, Beneficial and detrimental entanglement for quantum battery charging, AVS Quantum Sci. 6, 012001 (2024).
  32. G. Francica, Quantum advantage in batteries for Sachdev-Ye-Kitaev interactions, Phys. Rev. A 110, 062209 (2024).
  33. G. Francica, Erratum: Quantum advantage in batteries for Sachdev-Ye-Kitaev interactions [Phys. Rev. A 110, 062209 (2024)], Phys. Rev. A 111, 019901(E) (2025).
  34. R. Bhatia and C. Davis, A better bound on the variance, Am. Math. Mon. 107, 353 (2000).
  35. C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 78, 2690 (1997).
  36. G. E. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E 60, 2721 (1999).
  37. J. Kurchan, A quantum fluctuation theorem, arXiv:cond-mat/0007360.
  38. H. Tasaki, Jarzynski relations for quantum systems and some applications, arXiv:cond-mat/0009244.
  39. P. Talkner, E. Lutz, and P. Hänggi, Fluctuation theorems: Work is not an observable, Phys. Rev. E 75, 050102(R) (2007).
  40. M. Campisi, P. Hänggi, and P. Talkner, Colloquium: Quantum fluctuation relations: Foundations and applications, Rev. Mod. Phys. 83, 771 (2011).
  41. M. Perarnau-Llobet, E. Bäumer, K. V. Hovhannisyan, M. Huber, and A. Acin, No-go theorem for the characterization of work fluctuations in coherent quantum systems, Phys. Rev. Lett. 118, 070601 (2017).
  42. E. Bäumer, M. Lostaglio, M. Perarnau-Llobet, and R. Sampaio, Fluctuating work in coherent quantum systems: Proposals and limitations, in Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, edited by F. Binder, L. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer, Cham, 2018), Vol. 195.
  43. S. Gherardini and G. De Chiara, Quasiprobabilities in quantum thermodynamics and many-body systems, PRX Quantum 5, 030201 (2024).
  44. D. R. M. Arvidsson-Shukur, W. F. Braasch Jr., S. De Bièvre, J. Dressel, A. N. Jordan, C. Langrenez, M. Lostaglio, J. S. Lundeen, and N. Y. Halpern, Properties and applications of the Kirkwood–Dirac distribution, New J. Phys. 26, 121201 (2024).
  45. A. E. Allahverdyan, Nonequilibrium quantum fluctuations of work, Phys. Rev. E 90, 032137 (2014).
  46. P. Solinas and S. Gasparinetti, Full distribution of work done on a quantum system for arbitrary initial states, Phys. Rev. E 92, 042150 (2015).
  47. M. Lostaglio, A. Belenchia, A. Levy, S. Hernández-Gómez, N. Fabbri, and S. Gherardini, Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables, Quantum 7, 1128 (2023).
  48. M. Lostaglio, Quantum fluctuation theorems, contextuality, and work quasiprobabilities, Phys. Rev. Lett. 120, 040602 (2018).
  49. G. Francica, Class of quasiprobability distributions of work with initial quantum coherence, Phys. Rev. E 105, 014101 (2022).
  50. G. Francica, Most general class of quasiprobability distributions of work, Phys. Rev. E 106, 054129 (2022).
  51. G. Francica and L. Dell’Anna, Optimal work extraction from quantum batteries based on the expected utility hypothesis, Phys. Rev. E 109, 044119 (2024).
  52. G. Francica and L. Dell’Anna, Role of quantum correlations in daemonic expected utility, Phys. Rev. A 109, 052221 (2024).
  53. G. Francica and L. Dell’Anna, Work fluctuation theorems with initial quantum coherence, Phys. Rev. E 109, 064138 (2024).
  54. G. Francica and L. Dell’Anna, Quasiprobability distribution of work in the quantum Ising model, Phys. Rev. E 108, 014106 (2023).
  55. X. Chen, Z.-C. Gu, and X.-G. Wen, Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order, Phys. Rev. B 82, 155138 (2010).
  56. A. J. Leggett and A. Garg, Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Phys. Rev. Lett. 54, 857 (1985).
  57. H. J. D. Miller and J. Anders, Leggett-Garg inequalities for quantum fluctuating work, Entropy 20, 200 (2018).

Outline

Information

APS Open Sci. 1, 000093– Published 13 August, 2026
Vol. 1
  • Received 27 March 2025
  • Accepted 5 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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