- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Global-local duality of energetic control cost in multipartite quantum correlated systems

Rui Guan1, Junjie Liu2,1,*, and Jian-Hua Jiang3,4,5,†

  • *Contact author: jj_liu@shu.edu.cn
  • †Contact author: jhjiang3@ustc.edu.cn
PDF

Phys. Rev. Research 7, L022054 – Published 5 June, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022054

Abstract

Multipartite quantum correlated systems (MQCSs) are widely utilized in diverse quantum information tasks, where their sophisticated control inherently incurs energetic costs. However, the fundamental characteristics of these control costs remain elusive, largely due to the lack of thermodynamic descriptions capable of capturing the full complexities of MQCSs. Here, we uncover universal thermodynamic relations for arbitrary MQCSs weakly coupled to a thermal bath, establishing an intrinsic global-local duality of control costs. Using these relations, we elucidate the exact role of multipartite correlation—a defining quantum feature of MQCSs—in shaping control costs at finite times. We also demonstrate that the relative magnitude between global and local control costs is undetermined, which perplexes the cost management of MQCSs under finite-time controls. Our results are numerically corroborated with applications to experimentally realizable multiqubit systems undergoing finite-time qubit reset processes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (80)

  1. J. Gea-Banacloche, Minimum energy requirements for quantum computation, Phys. Rev. Lett. 89, 217901 (2002).
  2. A. Auffèves, Quantum technologies need a quantum energy initiative, PRX Quantum 3, 020101 (2022).
  3. L. Szilard, On the decrease in entropy in a thermodynamic system by the intervention of intelligent beings, Z. Phys. 53, 840 (1929).
  4. R. Landauer, Irreversibility and heat generation in the computing process, IBM J. Res. Dev. 5, 183 (1961).
  5. K. Maruyama, F. Nori, and V. Vedral, Colloquium: The physics of Maxwell's demon and information, Rev. Mod. Phys. 81, 1 (2009).
  6. J. Parrondo, J. Horowitz, and T. Sagawa, Thermodynamics of information, Nat. Phys. 11, 131 (2015).
  7. J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics—a topical review, J. Phys. A: Math. Theor. 49, 143001 (2016).
  8. J. Liu, J. Lu, C. Wang, and J.-H. Jiang, Inferring general links between energetics and information with unknown environment, Phys. Rev. Res. 6, 033202 (2024).
  9. G. Landi and M. Paternostro, Irreversible entropy production: From classical to quantum, Rev. Mod. Phys. 93, 035008 (2021).
  10. A. Danageozian, M. Wilde, and F. Buscemi, Thermodynamic constraints on quantum information gain and error correction: A triple trade-off, PRX Quantum 3, 020318 (2022).
  11. M. Nielsen, C. Caves, B. Schumacher, and H. Barnum, Information-theoretic approach to quantum error correction and reversible measurement, Proc. R. Soc. A 454, 277 (1998).
  12. T. Sagawa and M. Ueda, Minimal energy cost for thermodynamic information processing: Measurement and information erasure, Phys. Rev. Lett. 102, 250602 (2009).
  13. J. Horowitz and K. Jacobs, Energy cost of controlling mesoscopic quantum systems, Phys. Rev. Lett. 115, 130501 (2015).
  14. A. Boyd, D Mandal, and J. Crutchfield, Thermodynamics of modularity: Structural costs beyond the Landauer bound, Phys. Rev. X 8, 031036 (2018).
  15. O. Abah, R. Puebla, A. Kiely, G. De Chiara, M. Paternostro, and S. Campbell, Energetic cost of quantum control protocols, New J. Phys. 21, 103048 (2019).
  16. S. Deffner, Energetic cost of Hamiltonian quantum gates, Europhys. Lett. 134, 40002 (2021).
  17. A. Pearson, Y. Guryanova, P. Erker, E. Laird, G. Briggs, M. Huber, and N. Ares, Measuring the thermodynamic cost of timekeeping, Phys. Rev. X 11, 021029 (2021).
  18. G. Chiribella, F. Meng, R. Renner, and M. Yung, The nonequilibrium cost of accurate information processing, Nat. Commun. 13, 7155 (2022).
  19. M. Woods and M. Horodecki, Autonomous quantum devices: When are they realizable without additional thermodynamic costs? Phys. Rev. X 13, 011016 (2023).
  20. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  21. A. Chin, S. Huelga, and M. Plenio, Quantum metrology in non-Markovian environments, Phys. Rev. Lett. 109, 233601 (2012).
  22. I. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
  23. G. Adesso, T. Bromley, and M. Cianciaruso, Measures and applications of quantum correlations, J. Phys. A: Math. Theor. 49, 473001 (2016).
  24. C. Koch, Controlling open quantum systems: Tools, achievements, and limitations, J. Phys.: Condens. Matter 28, 213001 (2016).
  25. G. De Chiara and A. Sanpera, Genuine quantum correlations in quantum many-body systems: a review of recent progress, Rep. Prog. Phys. 81, 074002 (2018).
  26. F. Shahandeh, A. Lund, and T. Ralph, Quantum correlations and global coherence in distributed quantum computing, Phys. Rev. A 99, 052303 (2019).
  27. K. Head-Marsden, J. Flick, C. Ciccarino, and P. Narang, Quantum information and algorithms for correlated quantum matter, Chem. Rev. 121, 3061 (2021).
  28. J. Britton, B. Sawyer, A. Keith, C. Wang, J. Freericks, H. Uys, M. Biercuk, and J. Bollinger, Engineered two-dimensional ising interactions in a trapped-ion quantum simulator with hundreds of spins, Nature (London) 484, 489 (2012).
  29. H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models, Nature (London) 534, 667 (2016).
  30. C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Yao, Programmable quantum simulations of spin systems with trapped ions, Rev. Mod. Phys. 93, 025001 (2021).
  31. A. Periwal, E. Cooper, P. Kunkel, J. Wienand, E. Davis, and M. Schleier-Smith, Programmable interactions and emergent geometry in an array of atom clouds, Nature (London) 600, 630 (2021).
  32. F. Mivehvar, F. Piazza, T. Donner, and H. Ritsch, Cavity QED with quantum gases: new paradigms in many-body physics, Adv. Phys. 70, 1 (2021).
  33. J. Zwolak and J. Taylor, Colloquium: Advances in automation of quantum dot devices control, Rev. Mod. Phys. 95, 011006 (2023).
  34. X. Mi, A. Michailidis, S. Shabani, K. Miao, P. Klimov, J. Lloyd, E. Rosenberg, R. Acharya, I. Aleiner, T. I. Andersen et al., Stable quantum-correlated many-body states through engineered dissipation, Science 383, 1332 (2024).
  35. N. Defenu, T. Donner, T. Macrì, G. Pagano, S. Ruffo, and A. Trombettoni, Long-range interacting quantum systems, Rev. Mod. Phys. 95, 035002 (2023).
  36. L. Feng, O. Katz, C. Haack, M. Maghrebi, A. Gorshkov, Z. Gong, M. Cetina, and C. Monroe, Continuous symmetry breaking in a trapped-ion spin chain, Nature (London) 623, 713 (2023).
  37. T. Sagawa and M. Ueda, Fluctuation theorem with information exchange: Role of correlations in stochastic thermodynamics, Phys. Rev. Lett. 109, 180602 (2012).
  38. M. Bera, A. Riera, M. Lewenstein, and A. Winter, Generalized laws of thermodynamics in the presence of correlations, Nat. Commun. 8, 2180 (2017).
  39. F. Sapienza, F. Cerisola, and A. Roncaglia, Correlations as a resource in quantum thermodynamics, Nat. Commun. 10, 2492 (2019).
  40. J. Oppenheim, M. Horodecki, P. Horodecki, and R. Horodecki, Thermodynamical approach to quantifying quantum correlations, Phys. Rev. Lett. 89, 180402 (2002).
  41. M. Perarnau-Llobet, K. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, and A. Acín, Extractable work from correlations, Phys. Rev. X 5, 041011 (2015).
  42. G. Manzano, F. Plastina, and R. Zambrini, Optimal work extraction and thermodynamics of quantum measurements and correlations, Phys. Rev. Lett. 121, 120602 (2018).
  43. K. Micadei, J. Peterson, A. Souza, R. Sarthour, I. Oliveira, G. Landi, T. Batalhão, R. Serra, and E. Lutz, Reversing the direction of heat flow using quantum correlations, Nat. Commun. 10, 2456 (2019).
  44. P. Lipka-Bartosik, G. Diotallevi, and P. Bakhshinezhad, Fundamental limits on anomalous energy flows in correlated quantum systems, Phys. Rev. Lett. 132, 140402 (2024).
  45. M. Huber, M. Perarnau-Llobet, K. Hovhannisyan, P. Skrzypczyk, C. Klöckl, N. Brunner, and A. Acín, Thermodynamic cost of creating correlations, New J. Phys. 17, 065008 (2015).
  46. L. Rio, J. Åberg, R. Renner, O. Dahlsten, and V. Vedral, The thermodynamic meaning of negative entropy, Nature (London) 474, 61 (2011).
  47. B. Groisman, S. Popescu, and A. Winter, Quantum, classical, and total amount of correlations in a quantum state, Phys. Rev. A 72, 032317 (2005).
  48. K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, The classical-quantum boundary for correlations: Discord and related measures, Rev. Mod. Phys. 84, 1655 (2012).
  49. G. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E 60, 2721 (1999).
  50. S. Vaikuntanathan and C. Jarzynski, Dissipation and lag in irreversible processes, Europhys. Lett. 87, 60005 (2009).
  51. T. Sagawa and M. Ueda, Role of mutual information in entropy production under information exchanges, New J. Phys. 15, 125012 (2013).
  52. A. Barato, D. Hartich, and U. Seifert, Information-theoretic versus thermodynamic entropy production in autonomous sensory networks, Phys. Rev. E 87, 042104 (2013).
  53. J. Horowitz and M. Esposito, Thermodynamics with continuous information flow, Phys. Rev. X 4, 031015 (2014).
  54. A. Bruch, M. Thomas, S. Viola Kusminskiy, F. von Oppen, and A. Nitzan, Quantum thermodynamics of the driven resonant level model, Phys. Rev. B 93, 115318 (2016).
  55. L. Cangemi, M. Carrega, A. De Candia, V. Cataudella, G. De Filippis, M. Sassetti, and G. Benenti, Optimal energy conversion through antiadiabatic driving breaking time-reversal symmetry, Phys. Rev. Res. 3, 013237 (2021).
  56. J. Liu, K. Jung, and D. Segal, Periodically driven quantum thermal machines from warming up to limit cycle, Phys. Rev. Lett. 127, 200602 (2021).
  57. S. Deffner and C. Jarzynski, Information processing and the second law of thermodynamics: An inclusive, Hamiltonian approach, Phys. Rev. X 3, 041003 (2013).
  58. J. Liu and H. Nie, Universal Landauer-like inequality from the first law of thermodynamics, Phys. Rev. A 108, L040203 (2023).
  59. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022054 for additional theoretical analysis as well as numerical results that complement the main text.
  60. H. Miller, G. Guarnieri, M. Mitchison, and J. Goold, Quantum fluctuations hinder finite-time information erasure near the Landauer limit, Phys. Rev. Lett. 125, 160602 (2020).
  61. P. Riechers and M. Gu, Impossibility of achieving Landauer's bound for almost every quantum state, Phys. Rev. A 104, 012214 (2021).
  62. Y. Kandel, H. Qiao, S. Fallahi, G. Gardner, M. Manfra, and J. Nichol, Coherent spin-state transfer via Heisenberg exchange, Nature (London) 573, 553 (2019).
  63. A. Karamlou, J. Braumüller, Y. Yanay, A. Di Paolo, P. Harrington, B. Kannan, D. Kim, M. Kjaergaard, A. Melville, S. Muschinske, B. Niedzielski, A. Vepsäläinen, R. Winik, J. Yoder, M. Schwartz, C. Tahan, T. Orlando, S. Gustavsson, and W. Oliver, Quantum transport and localization in 1d and 2d tight-binding lattices, npj Quantum Inf. 8, 35 (2022).
  64. D. DiVincenzo, The physical implementation of quantum computation, Fortschr. Phys. 48, 771 (2000).
  65. P. Schindler, J. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, and R. Blatt, Experimental repetitive quantum error correction, Science 332, 1059 (2011).
  66. M. Reed, L. DiCarlo, S. E. Nigg, L. Sun, L. Frunzio, S. Girvin, and R. Schoelkopf, Realization of three-qubit quantum error correction with superconducting circuits, Nature (London) 482, 382 (2012).
  67. M. Cattaneo, G. Giorgi, S. Maniscalco, and R. Zambrini, Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation, New J. Phys. 21, 113045 (2019).
  68. B. Lanyon, C. Maier, M. Holzäpfel, T. Baumgratz, C. Hempel, P. Jurcevic, I. Dhand, A. S. Buyskikh, A. J. Daley, M. Cramer, M. Plenio, R. Blatt, and C. Roos, Efficient tomography of a quantum many-body system, Nat. Phys. 13, 1158 (2017).
  69. J. Yoneda, W. Huang, M. Feng, C. Yang, K. Chan, T. Tanttu, W. Gilbert, R. Leon, F. Hudson, K. Itoh, A. Morello, S. Bartlett, A. Laucht, A. Saraiva, and A. Dzurak, Coherent spin qubit transport in silicon, Nat. Commun. 12, 4114 (2021).
  70. Y. Zhong, H. Chang, A. Bienfait, E. Dumur, M. Chou, C. Conner, J. Grebel, R. Povey, H. Yan, D. Schuster, and A. Cleland, Deterministic multi-qubit entanglement in a quantum network, Nature (London) 590, 571 (2021).
  71. G. Torlai, G. Mazzola, J. Carrasquilla, M. Troyer, R. Melko, and G. Carleo, Neural-network quantum state tomography, Nat. Phys. 14, 447 (2018).
  72. S. Ahmed, C. Sánchez Muñoz, F. Nori, and A. Kockum, Quantum state tomography with conditional generative adversarial networks, Phys. Rev. Lett. 127, 140502 (2021).
  73. G. Struchalin, Ya. Zagorovskii, E. Kovlakov, S. Straupe, and S. Kulik, Experimental estimation of quantum state properties from classical shadows, PRX Quantum 2, 010307 (2021).
  74. G. Schaller, C. Nietner, and T. Brandes, Relaxation dynamics of meso-reservoirs, New J. Phys. 16, 125011 (2014).
  75. G. Amato, H.-P. Breuer, S. Wimberger, A. Rodríguez, and A. Buchleitner, Noninteracting many-particle quantum transport between finite reservoirs, Phys. Rev. A 102, 022207 (2020).
  76. A. Riera-Campeny, A. Sanpera, and P. Strasberg, Quantum systems correlated with a finite bath: Nonequilibrium dynamics and thermodynamics, PRX Quantum 2, 010340 (2021).
  77. J. Pekola and B. Karimi, Colloquium: Quantum heat transport in condensed matter systems, Rev. Mod. Phys. 93, 041001 (2021).
  78. H. Yuan, Y.-H. Ma, and C. Sun, Optimizing thermodynamic cycles with two finite-sized reservoirs, Phys. Rev. E 105, L022101 (2022).
  79. M. Spiecker, P. Paluch, N. Gosling, N. Drucker, S. Matityahu, D. Gusenkova, S. Günzler, D. Rieger, I. Takmakov, F. Valenti, P. Winkel, R. Gebauer, O. Sander, G. Catelani, A. Shnirman, A. Ustinov, W. Wernsdorfer, Y. Cohen, and I. Pop, Two-level system hyperpolarization using a quantum Szilard engine, Nat. Phys. 19, 1320 (2023).
  80. S. Moreira, P. Samuelsson, and P. Potts, Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir, Phys. Rev. Lett. 131, 220405 (2023).

Outline

Information

Phys. Rev. Research 7, L022054– Published 5 June, 2025
  • Received 22 December 2024
  • Revised 4 March 2025
  • Accepted 20 May 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation