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arxiv: 2509.13519 · v1 · pith:2BOZ6BEEnew · submitted 2025-09-16 · 🪐 quant-ph · cond-mat.stat-mech

Quantum speed limit for the OTOC from an open systems perspective

Devjyoti Tripathy , Juzar Thingna , Sebastian Deffner This is my paper

Pith reviewed 2026-05-21 21:32 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords OTOCquantum speed limitscramblingopen quantum systemsdecoherencemany-body physicsRenyi entropytransverse field Ising model
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The pith

The OTOC decay rate is lower-bounded by system-environment coupling strength and environmental correlation functions.

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

This paper derives a quantum speed limit for the out-of-time-ordered correlator that measures how fast quantum information scrambles. It uses the OTOC-Renyi-2 entropy theorem to recast closed-system scrambling as an effective decoherence process in an open system. The bound then follows directly from the strength of the system-environment coupling and the environment's two-point correlation functions. A reader would care because the result supplies a model-independent way to quantify the fastest possible rate of information delocalization in many-body systems.

Core claim

Employing the OTOC-Renyi-2 entropy theorem we derive a quantum speed limit for the OTOC, which sets a lower bound for the rate with which information can be scrambled. This bound becomes particularly tractable by describing the scrambling of information in a closed quantum system as an effective decoherence process of an open system interacting with an environment. We prove that decay of the OTOC can be bounded by the strength of the system-environment coupling and two-point environmental correlation functions, and we validate the bound numerically on the non-integrable transverse field Ising model.

What carries the argument

OTOC-Renyi-2 entropy theorem that maps closed-system scrambling onto an effective open-system decoherence process

Load-bearing premise

The OTOC-Renyi-2 entropy theorem supplies a valid mapping from closed-system scrambling to effective open-system decoherence for non-integrable many-body models.

What would settle it

A numerical or experimental measurement on the transverse field Ising model in which the OTOC decays faster than the rate set by the coupling strength and two-point correlation functions would falsify the bound.

Figures

Figures reproduced from arXiv: 2509.13519 by Devjyoti Tripathy, Juzar Thingna, Sebastian Deffner.

Figure 1
Figure 1. Figure 1: FIG. 1. Minimum value of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Rate of information scrambling in the ferromagnetic non [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. QSL for the antiferromagnetic non-integrable transverse [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. QSL for non-stationary ennvironment for the Ferromag [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Quantum Speed Limit for the ferromagnetic [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

Scrambling, the delocalization of initially localized quantum information, is commonly characterized by the out-of-time ordered correlator (OTOC). Employing the OTOC-Renyi-2 entropy theorem we derive a quantum speed limit for the OTOC, which sets an lower bound for the rate with which information can be scrambled. This bound becomes particularly tractable by describing the scrambling of information in a closed quantum system as an effective decoherence process of an open system interacting with an environment. We prove that decay of the OTOC can be bounded by the strength of the system-environment coupling and two-point environmental correlation functions. We validate our analytic bound numerically using the non-integrable transverse field Ising model. Our results provide a universal and model-agnostic quantitative framework for understanding the dynamical limits of information spreading across quantum many-body physics, condensed matter, and engineered quantum platforms.

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

2 major / 2 minor

Summary. The manuscript employs the OTOC-Renyi-2 entropy theorem to map closed-system scrambling dynamics onto an effective open-system decoherence process. From this mapping it derives a quantum speed limit that lower-bounds the decay rate of the OTOC by the system-environment coupling strength and two-point environmental correlation functions. The bound is stated to be model-agnostic and is validated numerically on the non-integrable transverse-field Ising model.

Significance. If the open-system mapping and the resulting bound hold without additional uncontrolled approximations, the work supplies a concrete, quantitative link between OTOC decay and open-system quantities that could be measured or computed independently. The numerical check on the TFIM provides a first test of practicality, though the absence of error bars or systematic finite-size scaling limits the strength of the validation.

major comments (2)
  1. [§2] §2 (OTOC-Renyi-2 entropy theorem application): the manuscript invokes the theorem to equate the OTOC with a decoherence factor whose time derivative is bounded by standard open-system terms, yet provides no derivation showing that the theorem remains exact or controlled when the 'environment' is replaced by the complement of a local subsystem in a non-integrable many-body chain. In this regime the two-point environmental correlators become intra-system operators whose own decay is governed by the scrambling dynamics the bound is intended to constrain; an explicit statement of the required assumptions (Markovianity, weak coupling, or controlled error terms) is needed for the central claim.
  2. [§3] §3 (derivation of the QSL): the bound is expressed directly in terms of the system-bath coupling and bath correlators, but the step that converts the time derivative of the mapped decoherence factor into the stated inequality is not shown in sufficient detail to confirm that no additional system-specific assumptions enter. A line-by-line expansion of this step, including the precise definition of the effective master-equation generator, would make the load-bearing step verifiable.
minor comments (2)
  1. [Figure 2] Figure 2: the numerical curves for the OTOC and the analytic bound are plotted without error bars or finite-size extrapolation; adding these would strengthen the validation claim.
  2. Notation: the symbol for the environmental two-point function is introduced without an explicit operator definition or Hilbert-space trace; a short clarifying sentence would remove ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments that help clarify the assumptions and derivations. We address each major comment below and will revise the manuscript accordingly to improve clarity and verifiability.

read point-by-point responses

  1. Referee: [§2] §2 (OTOC-Renyi-2 entropy theorem application): the manuscript invokes the theorem to equate the OTOC with a decoherence factor whose time derivative is bounded by standard open-system terms, yet provides no derivation showing that the theorem remains exact or controlled when the 'environment' is replaced by the complement of a local subsystem in a non-integrable many-body chain. In this regime the two-point environmental correlators become intra-system operators whose own decay is governed by the scrambling dynamics the bound is intended to constrain; an explicit statement of the required assumptions (Markovianity, weak coupling, or controlled error terms) is needed for the central claim.

    Authors: The OTOC-Renyi-2 entropy theorem provides an exact identity that maps the OTOC to the Renyi-2 entropy of an auxiliary state, which admits an interpretation as a decoherence factor without requiring Markovianity, weak coupling, or other approximations. When the complement of a local subsystem plays the role of the environment, the two-point correlators are indeed intra-system operators. Our bound is nevertheless well-defined because it is expressed directly in terms of these correlators; it does not presuppose their decay rate but rather constrains the OTOC decay rate by their magnitude. We agree that an explicit discussion of this point is warranted and will add a clarifying paragraph in Section 2 stating that the mapping is exact via the theorem, that no uncontrolled approximations are introduced, and that the bound remains valid in the many-body setting with the correlators treated as given quantities that can be computed or bounded separately. revision: yes

  2. Referee: [§3] §3 (derivation of the QSL): the bound is expressed directly in terms of the system-bath coupling and bath correlators, but the step that converts the time derivative of the mapped decoherence factor into the stated inequality is not shown in sufficient detail to confirm that no additional system-specific assumptions enter. A line-by-line expansion of this step, including the precise definition of the effective master-equation generator, would make the load-bearing step verifiable.

    Authors: We thank the referee for pointing out the need for greater detail. The conversion step applies a standard open-systems inequality (bounding the derivative of the decoherence factor by the norm of the effective interaction) to the time derivative of the mapped quantity. The effective generator is the commutator with the system-environment coupling Hamiltonian in the interaction picture. We will insert a line-by-line expansion of this step, either in the main text of Section 3 or in a new appendix, explicitly defining the generator and showing that the inequality follows from the general open-systems bound without introducing additional system-specific assumptions beyond the correlators themselves. revision: yes

Circularity Check

0 steps flagged

Derivation applies external OTOC-Renyi-2 theorem plus standard open-system QSL; bound expressed via independent coupling and correlator inputs

full rationale

The paper invokes the OTOC-Renyi-2 entropy theorem to recast closed-system scrambling as effective open-system decoherence, then derives a QSL inequality bounding OTOC decay rate by system-environment coupling strength and two-point bath correlators. These correlators enter as external inputs to the bound rather than being fitted to or defined from the OTOC itself. Numerical checks on the transverse-field Ising model compare the analytic bound against direct OTOC computation without parameter tuning or self-referential closure. No equation reduces the claimed lower bound to an identity with its inputs by construction, and no load-bearing step collapses to a self-citation chain or ansatz smuggled from prior author work. The result is therefore self-contained against the stated external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The derivation rests on the OTOC-Renyi-2 entropy theorem (treated as given) and on the validity of the effective open-system description for closed many-body dynamics. No new free parameters or invented entities are introduced in the abstract; the bound is expressed in terms of coupling strength and environmental correlators that are assumed measurable or computable.

axioms (2)
  • domain assumption OTOC-Renyi-2 entropy theorem holds for the systems under study
    Invoked to convert the scrambling problem into an effective decoherence process.
  • domain assumption Closed-system scrambling can be faithfully represented as open-system decoherence with a fictitious environment
    Central modeling step that allows use of open-systems bounds.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes

    quant-ph 2025-09 unverdicted novelty 5.0

    Derives QSLs based on square roots of Jensen-Shannon and Jeffreys divergences, expressed via Schatten speed and eigenvalue cost functions, for general quantum processes including unitary evolution and specific open channels.

Reference graph

Works this paper leans on

120 extracted references · 120 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    Heisenberg, Über den anschaulichen Inhalt der quan- tentheoretischen Kinematik und Mechanik, Zeitschrift fur Physik43, 172 (1927)

    W. Heisenberg, Über den anschaulichen Inhalt der quan- tentheoretischen Kinematik und Mechanik, Zeitschrift fur Physik43, 172 (1927)

    work page 1927

  2. [2]

    H. P. Robertson, The uncertainty principle, Phys. Rev.34, 163 (1929)

    work page 1929

  3. [3]

    Messiah,Quantum mechanics(Courier Corporation, 2014)

    A. Messiah,Quantum mechanics(Courier Corporation, 2014). 6

    work page 2014

  4. [4]

    E. L. Hahn, Spin echoes, Phys. Rev.80, 580 (1950)

    work page 1950

  5. [5]

    Swingle, Unscrambling the physics of out-of-time-order correlators, Nat

    B. Swingle, Unscrambling the physics of out-of-time-order correlators, Nat. Phys.14, 988 (2018)

    work page 2018

  6. [6]

    D. A. Roberts and B. Swingle, Lieb-robinson bound and the butterfly effect in quantum field theories, Phys. Rev. Lett.117, 091602 (2016)

    work page 2016

  7. [7]

    Huang, Y .-L

    Y . Huang, Y .-L. Zhang, and X. Chen, Out-of-time-ordered correlators in many-body localized systems, Ann. Phys. 529, 1600318 (2017)

    work page 2017

  8. [8]

    Zhu, Z.-H

    Q. Zhu, Z.-H. Sun, M. Gong, F. Chen, Y .-R. Zhang, Y . Wu, Y . Ye, C. Zha, S. Li, S. Guo,et al., Observation of thermal- ization and information scrambling in a superconducting quantum processor, Phys. Rev. Lett.128, 160502 (2022)

    work page 2022

  9. [9]

    K. A. Landsman, C. Figgatt, T. Schuster, N. M. Linke, B. Yoshida, N. Y . Yao, and C. Monroe, Verified quantum information scrambling, Nature567, 61 (2019)

    work page 2019

  10. [10]

    Gärttner, J

    M. Gärttner, J. G. Bohnet, A. Safavi-Naini, M. L. Wall, J. J. Bollinger, and A. M. Rey, Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet, Nat. Phys.13, 781 (2017)

    work page 2017

  11. [11]

    Yunger Halpern, Jarzynski-like equality for the out-of- time-ordered correlator, Phys

    N. Yunger Halpern, Jarzynski-like equality for the out-of- time-ordered correlator, Phys. Rev. A95, 012120 (2017)

    work page 2017

  12. [12]

    Touil and S

    A. Touil and S. Deffner, Information scrambling – a quantum thermodynamic perspective, Europhys. Lett.146, 48001 (2024)

    work page 2024

  13. [13]

    Touil and S

    A. Touil and S. Deffner, Information scrambling ver- sus decoherence—two competing sinks for entropy, PRX Quantum2, 010306 (2021)

    work page 2021

  14. [14]

    Anand and P

    N. Anand and P. Zanardi, BROTOCs and Quantum Infor- mation Scrambling at Finite Temperature, Quantum6, 746 (2022)

    work page 2022

  15. [15]

    Yuan, S.-Y

    D. Yuan, S.-Y . Zhang, Y . Wang, L.-M. Duan, and D.-L. Deng, Quantum information scrambling in quantum many- body scarred systems, Phys. Rev. Res.4, 023095 (2022)

    work page 2022

  16. [17]

    M. S. Blok, V . V . Ramasesh, T. Schuster, K. O’Brien, J. M. Kreikebaum, D. Dahlen, A. Morvan, B. Yoshida, N. Y . Yao, and I. Siddiqi, Quantum information scrambling on a superconducting qutrit processor, Phys. Rev. X11, 021010 (2021)

    work page 2021

  17. [18]

    Zanardi, E

    P. Zanardi, E. Dallas, F. Andreadakis, and S. Lloyd, Op- erational Quantum Mereology and Minimal Scrambling, Quantum8, 1406 (2024)

    work page 2024

  18. [19]

    Dallas, F

    E. Dallas, F. Andreadakis, and P. Zanardi, A butter- fly effect in encoding-decoding quantum circuits (2024), arXiv:2409.16481

    work page arXiv 2024

  19. [20]

    Andreadakis, E

    F. Andreadakis, E. Dallas, and P. Zanardi, Long-time quan- tum scrambling and generalized tensor product structures, Phys. Rev. A109, 052424 (2024)

    work page 2024

  20. [21]

    Andreadakis, N

    F. Andreadakis, N. Anand, and P. Zanardi, Scrambling of algebras in open quantum systems, Phys. Rev. A107, 042217 (2023)

    work page 2023

  21. [22]

    Zanardi, Quantum scrambling of observable algebras, Quantum6, 666 (2022)

    P. Zanardi, Quantum scrambling of observable algebras, Quantum6, 666 (2022)

    work page 2022

  22. [23]

    Zanardi and N

    P. Zanardi and N. Anand, Information scrambling and chaos in open quantum systems, Phys. Rev. A103, 062214 (2021)

    work page 2021

  23. [24]

    Andreadakis, E

    F. Andreadakis, E. Dallas, and P. Zanardi, Operator space entangling power of quantum dynamics and local operator entanglement growth in dual-unitary circuits, Phys. Rev. A 110, 052416 (2024)

    work page 2024

  24. [25]

    A. S. Matsoukas-Roubeas, T. Prosen, and A. d. Campo, Quantum Chaos and Coherence: Random Parametric Quantum Channels, Quantum8, 1446 (2024)

    work page 2024

  25. [26]

    Martinez-Azcona, A

    P. Martinez-Azcona, A. Kundu, A. del Campo, and A. Chenu, Stochastic operator variance: An observable to diagnose noise and scrambling, Phys. Rev. Lett.131, 160202 (2023)

    work page 2023

  26. [27]

    Lo Monaco, L

    G. Lo Monaco, L. Innocenti, D. Cilluffo, D. A. Chisholm, S. Lorenzo, and G. Massimo Palma, An operational defi- nition of quantum information scrambling, Quantum Sci. Technol.10, 015055 (2024)

    work page 2024

  27. [28]

    Hosur, X.-L

    P. Hosur, X.-L. Qi, D. A. Roberts, and B. Yoshida, Chaos in quantum channels, J. High Energy Phys.2016(2), 4

    work page 2016

  28. [29]

    S. H. Shenker and D. Stanford, Black holes and the butter- fly effect, J. High Energy Phys.2014(3), 67

    work page 2014

  29. [30]

    Hayden and J

    P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, J. High Energy Phys. 2007(09), 120

    work page 2007

  30. [31]

    Goldfriend and J

    T. Goldfriend and J. Kurchan, Quasi-integrable systems are slow to thermalize but may be good scramblers, Phys. Rev. E102, 022201 (2020)

    work page 2020

  31. [32]

    Xu and B

    S. Xu and B. Swingle, Scrambling dynamics and out-of- time-ordered correlators in quantum many-body systems, PRX Quantum5, 010201 (2024)

    work page 2024

  32. [33]

    H. Shen, P. Zhang, Y .-Z. You, and H. Zhai, Information scrambling in quantum neural networks, Phys. Rev. Lett. 124, 200504 (2020)

    work page 2020

  33. [34]

    Barch, N

    B. Barch, N. Anand, J. Marshall, E. Rieffel, and P. Za- nardi, Scrambling and operator entanglement in local non- hermitian quantum systems, Phys. Rev. B108, 134305 (2023)

    work page 2023

  34. [35]

    Giorda and P

    P. Giorda and P. Zanardi, Quantum chaos and operator fi- delity metric, Phys. Rev. E81, 017203 (2010)

    work page 2010

  35. [36]

    Grabarits, K

    A. Grabarits, K. R. Swain, M. S. Heydari, P. Chandarana, F. J. Gómez-Ruiz, and A. del Campo, Quantum chaos in random ising networks, Phys. Rev. Res.7, 013146 (2025)

    work page 2025

  36. [37]

    A. K. Das, C. Cianci, D. G. A. Cabral, D. A. Zarate-Herrada, P. Pinney, S. Pilatowsky-Cameo, A. S. Matsoukas-Roubeas, V . S. Batista, A. del Campo, E. J. Torres-Herrera, and L. F. Santos, Proposal for many- body quantum chaos detection, Phys. Rev. Res.7, 013181 (2025)

    work page 2025

  37. [38]

    P. H. S. Bento, A. del Campo, and L. C. Céleri, Krylov complexity and dynamical phase transition in the quenched lipkin-meshkov-glick model, Phys. Rev. B109, 224304 (2024)

    work page 2024

  38. [39]

    Z. Cao, Z. Xu, and A. del Campo, Probing quantum chaos in multipartite systems, Phys. Rev. Res.4, 033093 (2022)

    work page 2022

  39. [40]

    Z. Xu, A. Chenu, T. c. v. Prosen, and A. del Campo, Ther- mofield dynamics: Quantum chaos versus decoherence, Phys. Rev. B103, 064309 (2021)

    work page 2021

  40. [41]

    Chenu, J

    A. Chenu, J. Molina-Vilaplana, and A. del Campo, Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems, Quantum3, 127 (2019)

    work page 2019

  41. [42]

    Z. Xu, L. P. García-Pintos, A. Chenu, and A. del Campo, Extreme decoherence and quantum chaos, Phys. Rev. Lett. 122, 014103 (2019)

    work page 2019

  42. [43]

    Chenu, I

    A. Chenu, I. L. Egusquiza, J. Molina-Vilaplana, and A. del Campo, Quantum work statistics, loschmidt echo and in- 7 formation scrambling, Sci Rep8, 12634 (2018)

    work page 2018

  43. [44]

    M. F. Cavalcante, M. V . S. Bonança, E. Miranda, and S. Deffner, Emergence ofxstates in a quantum impurity model, Phys. Rev. Res.7, L022027 (2025)

    work page 2025

  44. [45]

    Carolan, A

    E. Carolan, A. Kiely, S. Campbell, and S. Deffner, Oper- ator growth and spread complexity in open quantum sys- tems, Europhys. Lett.147, 38002 (2024)

    work page 2024

  45. [46]

    Tripathy, A

    D. Tripathy, A. Touil, B. Gardas, and S. Deffner, Quantum information scrambling in two-dimensional bose–hubbard lattices, Chaos34, 043121 (2024)

    work page 2024

  46. [47]

    Hallam, J

    A. Hallam, J. G. Morley, and A. G. Green, The lya- punov spectra of quantum thermalisation, Nat. Commun. 10, 2708 (2019)

    work page 2019

  47. [48]

    Pilatowsky-Cameo, J

    S. Pilatowsky-Cameo, J. Chávez-Carlos, M. A. Bastarrachea-Magnani, P. Stránský, S. Lerma-Hernández, L. F. Santos, and J. G. Hirsch, Positive quantum lyapunov exponents in experimental systems with a regular classical limit, Phys. Rev. E101, 010202 (2020)

    work page 2020

  48. [49]

    Maldacena, S

    J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys.2016(8), 106

    work page 2016

  49. [50]

    A. M. García-García, J. J. M. Verbaarschot, and J.-p. Zheng, Lyapunov exponent as a signature of dissipative many-body quantum chaos, Phys. Rev. D110, 086010 (2024)

    work page 2024

  50. [51]

    Mandelstam and I

    L. Mandelstam and I. Tamm, The uncertainty relation be- tween energy and time in non-relativistic quantum me- chanics, inSelected Papers, edited by B. M. Bolotovskii, V . Y . Frenkel, and R. Peierls (Springer Berlin Heidelberg, Berlin, Heidelberg, 1991) pp. 115–123

    work page 1991

  51. [52]

    K. Funo, N. Shiraishi, and K. Saito, Speed limit for open quantum systems, New J. Phys.21, 013006 (2019)

    work page 2019

  52. [53]

    D. C. Brody and B. Longstaff, Evolution speed of open quantum dynamics, Phys. Rev. Res.1, 033127 (2019)

    work page 2019

  53. [54]

    Deffner and E

    S. Deffner and E. Lutz, Quantum speed limit for non- markovian dynamics, Phys. Rev. Lett.111, 010402 (2013)

    work page 2013

  54. [55]

    del Campo, I

    A. del Campo, I. L. Egusquiza, M. B. Plenio, and S. F. Huelga, Quantum speed limits in open system dynamics, Phys. Rev. Lett.110, 050403 (2013)

    work page 2013

  55. [56]

    Giovannetti, S

    V . Giovannetti, S. Lloyd, and L. Maccone, Quantum limits to dynamical evolution, Phys. Rev. A67, 052109 (2003)

    work page 2003

  56. [57]

    Deffner and E

    S. Deffner and E. Lutz, Energy–time uncertainty relation for driven quantum systems, J. Phys. A: Math. Theor.46, 335302 (2013)

    work page 2013

  57. [58]

    Uhlmann, An energy dispersion estimate, Phys

    A. Uhlmann, An energy dispersion estimate, Phys. Lett. A 161, 329 (1992)

    work page 1992

  58. [59]

    Pfeifer, How fast can a quantum state change with time?, Phys

    P. Pfeifer, How fast can a quantum state change with time?, Phys. Rev. Lett.70, 3365 (1993)

    work page 1993

  59. [60]

    Batle, M

    J. Batle, M. Casas, A. Plastino, and A. R. Plastino, Con- nection between entanglement and the speed of quantum evolution, Phys. Rev. A72, 032337 (2005)

    work page 2005

  60. [61]

    Rudnicki, Quantum speed limit and geometric measure of entanglement, Phys

    L. Rudnicki, Quantum speed limit and geometric measure of entanglement, Phys. Rev. A104, 032417 (2021)

    work page 2021

  61. [62]

    Mohan, S

    B. Mohan, S. Das, and A. K. Pati, Quantum speed limits for information and coherence, New J. Phys.24, 065003 (2022)

    work page 2022

  62. [63]

    Hamazaki, Quantum velocity limits for multiple observ- ables: Conservation laws, correlations, and macroscopic systems, Phys

    R. Hamazaki, Quantum velocity limits for multiple observ- ables: Conservation laws, correlations, and macroscopic systems, Phys. Rev. Res.6, 013018 (2024)

    work page 2024

  63. [64]

    Mohan and A

    B. Mohan and A. K. Pati, Quantum speed limits for ob- servables, Phys. Rev. A106, 042436 (2022)

    work page 2022

  64. [65]

    Aifer, J

    M. Aifer, J. Thingna, and S. Deffner, Energetic cost for speedy synchronization in non-hermitian quantum dynam- ics, Phys. Rev. Lett.133, 020401 (2024)

    work page 2024

  65. [66]

    Hörnedal, N

    N. Hörnedal, N. Carabba, A. S. Matsoukas-Roubeas, and A. del Campo, Ultimate speed limits to the growth of op- erator complexity, Commun. Phys.5, 207 (2022)

    work page 2022

  66. [67]

    Gill and T

    A. Gill and T. Sarkar, Speed limits and scrambling in krylov space (2024), arXiv:2408.06855

    work page arXiv 2024

  67. [68]

    Bhattacharya, P

    A. Bhattacharya, P. P. Nath, and H. Sahu, Speed limits to the growth of krylov complexity in open quantum systems, Phys. Rev. D109, L121902 (2024)

    work page 2024

  68. [69]

    Lloyd, Ultimate physical limits to computation, Nature 406, 1047 (2000)

    S. Lloyd, Ultimate physical limits to computation, Nature 406, 1047 (2000)

    work page 2000

  69. [70]

    Van Vu and K

    T. Van Vu and K. Saito, Topological speed limit, Phys. Rev. Lett.130, 010402 (2023)

    work page 2023

  70. [71]

    P. M. Poggi, S. Campbell, and S. Deffner, Diverging quan- tum speed limits: A herald of classicality, PRX Quantum 2, 040349 (2021)

    work page 2021

  71. [72]

    M. R. Frey, Quantum speed limits—primer, perspectives, and potential future directions, Quantum Inf Process15, 3919 (2016)

    work page 2016

  72. [73]

    Aifer and S

    M. Aifer and S. Deffner, From quantum speed limits to energy-efficient quantum gates, New J. Phys.24, 055002 (2022)

    work page 2022

  73. [74]

    Silva Pratapsi, S

    S. Silva Pratapsi, S. Deffner, and S. Gherardini, Quantum speed limit for kirkwood–dirac quasiprobabilities, Quan- tum Sci. Technol.10, 035019 (2025)

    work page 2025

  74. [75]

    Deffner, Nonlinear speed-ups in ultracold quantum gases, Europhys

    S. Deffner, Nonlinear speed-ups in ultracold quantum gases, Europhys. Lett.140, 48001 (2022)

    work page 2022

  75. [76]

    Deffner, Quantum speed-limited depletion of physical resources, Quantum Views5, 55 (2021)

    S. Deffner, Quantum speed-limited depletion of physical resources, Quantum Views5, 55 (2021)

    work page 2021

  76. [77]

    Deffner, Quantum speed limits and the maximal rate of information production, Phys

    S. Deffner, Quantum speed limits and the maximal rate of information production, Phys. Rev. Res.2, 013161 (2020)

    work page 2020

  77. [78]

    Kubo, Statistical mechanical theory of irreversible pro- cesses

    R. Kubo, Statistical mechanical theory of irreversible pro- cesses. 1. General theory and simple applications in mag- netic and conduction problems, J. Phys. Soc. Jpn.12, 570 (1957)

    work page 1957

  78. [79]

    Bocini, F

    S. Bocini, F. Caleca, F. Mezzacapo, and T. Roscilde, Nonlocal quench spectroscopy of fermionic excitations in quantum spin chains, Phys. Rev. B111, L121114 (2025)

    work page 2025

  79. [80]

    Schweigler, V

    T. Schweigler, V . Kasper, S. Erne, I. Mazets, B. Rauer, F. Cataldini, T. Langen, T. Gasenzer, J. Berges, and J. Schmiedmayer, Experimental characterization of a quantum many-body system via higher-order correlations, Nature545, 323 (2017)

    work page 2017

  80. [81]

    Zhang, G

    T. Zhang, G. Smith, J. A. Smolin, L. Liu, X.-J. Peng, Q. Zhao, D. Girolami, X. Ma, X. Yuan, and H. Lu, Quan- tification of entanglement and coherence with purity detec- tion, npj Quantum Inf.10, 60 (2024)

    work page 2024

Showing first 80 references.