pith. sign in

arxiv: 2604.14098 · v1 · submitted 2026-04-15 · 🪐 quant-ph

Protecting Heisenberg scaling in quantum metrology via engineered dressed states

Wojciech Gorecki , Christiane P. Koch This is my paper

Pith reviewed 2026-05-10 13:37 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum metrologyHeisenberg scalingdressed statesnoise suppressionNV centersquantum sensingopen quantum systemsLindblad operators
0
0 comments X

The pith

Dressed states generated by static fields can protect Heisenberg scaling in quantum metrology against low-temperature noise precisely when the signal generator lies outside the span of the noise coupling operators.

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

The paper establishes that static control fields can dress the states of a quantum sensor so that environmental noise fails to degrade the precision to a mere constant factor above the classical limit. Success hinges on a linear-algebra condition: the operator that encodes the signal must not lie in the span of the operators that couple the system to the bath. When this holds, the dressed dynamics allow the full Heisenberg scaling of uncertainty with the number of particles or time. The result applies even in systems where the bare Hamiltonian would violate the usual Lindblad-span criterion, and the authors demonstrate the idea with nitrogen-vacancy-center thermometry under magnetic fluctuations.

Core claim

For low-temperature noise, Heisenberg scaling is achievable if and only if the signal generator lies outside the linear span of the system-environment coupling operators. Engineered dressed states produced by static fields can satisfy this condition even when the undressed system does not, thereby restoring the full quantum advantage in precision.

What carries the argument

Dressed states created by static fields, which rotate the effective signal and noise operators so that the signal generator falls outside the span of the transformed coupling operators.

If this is right

  • Heisenberg scaling survives low-temperature noise whenever the dressed signal operator avoids the noise span.
  • The standard no-go criterion evaluated on the bare Hamiltonian can be circumvented by static dressing.
  • The same dressing strategy applies directly to other platforms once their coupling operators and signal generators are identified.
  • Spectral properties of the bath determine whether a given static field succeeds in placing the signal outside the noise span.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Design rules for static fields could be derived by optimizing the angle that maximizes the distance between the signal vector and the noise subspace.
  • The same linear-span test may guide control strategies in other open-system sensing tasks such as magnetometry or frequency estimation.
  • Extension to finite-temperature baths would require checking whether thermal excitation terms can be similarly rotated out of the signal direction.

Load-bearing premise

The bath must be at low temperature so that its spectral density permits a static-field transformation that moves the signal operator outside the span of the effective noise operators.

What would settle it

Measure the scaling of thermometric precision in an NV-center sensor under controlled magnetic noise, with and without an applied static field chosen to dress the states; the dressed case should recover 1/N scaling while the undressed case remains constant-factor limited.

Figures

Figures reproduced from arXiv: 2604.14098 by Christiane P. Koch, Wojciech Gorecki.

Figure 1
Figure 1. Figure 1: FIG. 1. Possibility of achieving Heisenberg scaling (HS) in quan [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

Quantum metrology promises precision beyond classical limits but environmental noise, unless properly controlled, reduces the quantum advantage to at most a constant improvement. A key challenge is therefore to design quantum control strategies that suppress noise while preserving sensitivity to the targeted signal. Here, we suggest to use dressed states generated by static fields to achieve this goal and show that success of this strategy depends on the spectral properties of the environment. For low-temperature noise, we show that Heisenberg scaling can be achieved if and only if the signal generator lies outside the linear span of the system-environment coupling operators. This implies that the proper dressed states may enable Heisenberg scaling even in cases where the well-known Hamiltonian-not-in-Lindblad-span criterion, evaluated without dressing, would forbid it. We illustrate dressed state metrology for the example of NV-center thermometry under magnetic-field fluctuations, with the framework readily applicable to other 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 / 1 minor

Summary. The manuscript proposes using dressed states generated by static fields to protect Heisenberg scaling in quantum metrology against environmental noise. For low-temperature baths, it claims an if-and-only-if result: Heisenberg scaling is achievable precisely when the signal generator lies outside the linear span of the (dressed) system-environment coupling operators. This can enable scaling even when the standard undressed Hamiltonian-not-in-Lindblad-span criterion would prohibit it. The approach is illustrated for NV-center thermometry under magnetic fluctuations and stated to be applicable to other platforms.

Significance. If the if-and-only-if condition holds with the stated generality, the work supplies a concrete design principle for restoring quantum advantage via static dressing in regimes where conventional criteria fail. The low-temperature spectral-density assumption is explicitly identified as the enabling condition, and the NV-center example demonstrates a concrete case where dressing succeeds where the undressed test would not. No machine-checked proofs or reproducible code are supplied, but the result is falsifiable via the spectral condition and the span test.

major comments (2)
  1. [Abstract] Abstract: the if-and-only-if theorem is asserted without any derivation steps, explicit Lindblad operators, or error analysis shown in the abstract (or referenced sections). The central claim that dressing can rotate the effective noise span to exclude the signal generator is load-bearing for the entire result; its soundness cannot be assessed from the given text.
  2. [Abstract] Abstract and illustration section: the result is conditioned on the bath spectral density J(ω) at low temperature permitting the static-field unitary to place the signal generator outside the span of the dressed Lindblad operators. No general criterion is supplied for which classes of spectra (Ohmic, sub-Ohmic, 1/f, etc.) satisfy this after dressing; only a single NV-center magnetic-fluctuation example is given. This directly limits the claimed practical advantage over the undressed criterion.
minor comments (1)
  1. [Abstract] Abstract: 'suggest to use' should read 'suggest using'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of the work and the constructive comments. We address each major point below with clarifications from the manuscript and proposed revisions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the if-and-only-if theorem is asserted without any derivation steps, explicit Lindblad operators, or error analysis shown in the abstract (or referenced sections). The central claim that dressing can rotate the effective noise span to exclude the signal generator is load-bearing for the entire result; its soundness cannot be assessed from the given text.

    Authors: The abstract is necessarily concise due to length limits, but the full if-and-only-if theorem, including the explicit form of the dressed Lindblad operators obtained via the static unitary dressing and the error analysis bounding the deviation from Heisenberg scaling, is derived in Sections III and IV. The proof relies on the low-temperature Markovian master equation where the effective noise operators are the dressed system-environment couplings, and shows that the quantum Fisher information retains the Heisenberg scaling precisely when the signal generator lies outside their linear span. To improve readability, we will revise the abstract to reference these sections and briefly state the span condition. revision: partial

  2. Referee: [Abstract] Abstract and illustration section: the result is conditioned on the bath spectral density J(ω) at low temperature permitting the static-field unitary to place the signal generator outside the span of the dressed Lindblad operators. No general criterion is supplied for which classes of spectra (Ohmic, sub-Ohmic, 1/f, etc.) satisfy this after dressing; only a single NV-center magnetic-fluctuation example is given. This directly limits the claimed practical advantage over the undressed criterion.

    Authors: The if-and-only-if result is general for any spectral density J(ω) under the low-temperature assumption, where the bath correlations are evaluated at the frequencies shifted by the dressing unitary; the span test is then applied to the resulting dressed Lindblad operators. The NV-center example demonstrates a concrete case (magnetic fluctuations with a spectrum allowing the dressing to exclude the signal) where the undressed criterion fails but the dressed one succeeds. While an exhaustive classification of all possible spectra is beyond the scope of a single paper, we will add a dedicated paragraph in the discussion section analyzing the condition for standard classes (Ohmic, sub-Ohmic, and 1/f noise), including the parameter regimes in which dressing restores the scaling. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central iff condition derived as general operator-span property

full rationale

The paper's core claim is a mathematical if-and-only-if statement for low-temperature noise: Heisenberg scaling holds precisely when the signal generator lies outside the linear span of the dressed system-environment coupling operators. This is framed as following from the structure of the effective Lindblad operators after the static-field unitary transformation, not from any fitted parameter, self-referential definition, or load-bearing self-citation. The NV-center thermometry example is presented as an illustration of the general framework rather than the origin of the result. No ansatz is smuggled via citation, no known empirical pattern is merely renamed, and the spectral-density prerequisite is stated explicitly as an assumption without being circularly presupposed to hold for all baths. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The result rests on the domain assumption of low-temperature noise whose spectrum permits the dressed-state decoupling; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Low-temperature noise with spectral density that vanishes at the relevant dressed frequencies
    Invoked to obtain the if-and-only-if condition for Heisenberg scaling.
  • standard math Markovian master equation in Lindblad form after dressing
    Underlying the linear-span criterion used throughout.

pith-pipeline@v0.9.0 · 5443 in / 1282 out tokens · 55731 ms · 2026-05-10T13:37:04.938581+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

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

  1. Precision limits for time-dependent quantum metrology under Markovian noise

    quant-ph 2026-05 unverdicted novelty 7.0

    Derives differential upper bounds on quantum Fisher information for time-dependent metrology under Markovian noise and proves universal long-time scaling laws saturated by quantum error correction.

Reference graph

Works this paper leans on

91 extracted references · 91 canonical work pages · cited by 1 Pith paper

  1. [1]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys.89, 035002 (2017)

    work page 2017

  2. [2]

    Z. Ma, P. Gokhale, T.-X. Zheng, S. Zhou, X. Yu, L. Jiang, P. Maurer, and F. T. Chong, Adaptive circuit learning for quan- tum metrology, in2021 IEEE International Conference on Quantum Computing and Engineering (QCE)(IEEE, 2021) pp. 419–430

    work page 2021

  3. [3]

    C. D. Marciniak, T. Feldker, I. Pogorelov, R. Kaubruegger, D. V . Vasilyev, R. van Bijnen, P. Schindler, P. Zoller, R. Blatt, and T. Monz, Optimal metrology with programmable quantum sensors, Nature603, 604 (2022)

    work page 2022

  4. [4]

    Q. Liu, Z. Hu, H. Yuan, and Y . Yang, Fully-optimized quan- tum metrology: framework, tools, and applications, Advanced Quantum Technologies7, 2400094 (2024)

    work page 2024

  5. [5]

    Hern ´andez-G´omez, F

    S. Hern ´andez-G´omez, F. Balducci, G. Fasiolo, P. Cappellaro, N. Fabbri, and A. Scardicchio, Optimal control of a quantum sensor: A fast algorithm based on an analytic solution, SciPost Physics17, 004 (2024)

    work page 2024

  6. [6]

    Kurdziałek, P

    S. Kurdziałek, P. Dulian, J. Majsak, S. Chakraborty, and R. Demkowicz-Dobrza ´nski, Quantum metrology using quan- tum combs and tensor network formalism, New Journal of Physics27, 013019 (2025)

    work page 2025

  7. [7]

    Giovannetti, S

    V . Giovannetti, S. Lloyd, and L. Maccone, Advances in quan- tum metrology, Nat. Photonics5, 222 (2011)

    work page 2011

  8. [8]

    T ´oth and I

    G. T ´oth and I. Apellaniz, Quantum metrology from a quantum information science perspective, Journal of Physics A: Mathe- matical and Theoretical47, 424006 (2014)

    work page 2014

  9. [9]

    Liu and H

    J. Liu and H. Yuan, Quantum parameter estimation with optimal control, Physical Review A96, 012117 (2017)

    work page 2017

  10. [10]

    Huang , author M

    J. Huang, M. Zhuang, and C. Lee, Entanglement-enhanced quantum metrology: From standard quantum limit to heisen- berg limit, Applied Physics Reviews11, 10.1063/5.0204102 (2024)

    work page doi:10.1063/5.0204102 2024

  11. [11]

    Bloom, T

    B. Bloom, T. Nicholson, J. Williams, S. Campbell, M. Bishof, X. Zhang, W. Zhang, S. Bromley, and J. Ye, An optical lattice clock with accuracy and stability at the 10- 18 level, Nature506, 71 (2014)

    work page 2014

  12. [12]

    A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Optical atomic clocks, Reviews of Modern Physics87, 637 (2015)

    work page 2015

  13. [13]

    T. L. Nicholson, S. Campbell, R. Hutson, G. E. Marti, B. Bloom, R. L. McNally, W. Zhang, M. Barrett, M. S. Safronova, G. Strouse,et al., Systematic evaluation of an atomic clock at 2×10- 18 total uncertainty, Nature commu- nications6, 6896 (2015)

    work page 2015

  14. [14]

    S. L. Campbell, R. Hutson, G. Marti, A. Goban, N. Dark- wah Oppong, R. McNally, L. Sonderhouse, J. Robinson, W. Zhang, B. Bloom,et al., A fermi-degenerate three- dimensional optical lattice clock, Science358, 90 (2017)

    work page 2017

  15. [15]

    Zhang, T

    C. Zhang, T. Ooi, J. S. Higgins, J. F. Doyle, L. von der Wense, K. Beeks, A. Leitner, G. A. Kazakov, P. Li, P. G. Thirolf,et al., Frequency ratio of the 229mth nuclear isomeric transition and the 87sr atomic clock, Nature633, 63 (2024)

    work page 2024

  16. [16]

    Bothwell, C

    T. Bothwell, C. J. Kennedy, A. Aeppli, D. Kedar, J. M. Robin- son, E. Oelker, A. Staron, and J. Ye, Resolving the gravitational redshift across a millimetre-scale atomic sample, Nature602, 420 (2022)

    work page 2022

  17. [17]

    Bongs, M

    K. Bongs, M. Holynski, J. V ovrosh, P. Bouyer, G. Condon, E. Rasel, C. Schubert, W. P. Schleich, and A. Roura, Taking atom interferometric quantum sensors from the laboratory to real-world applications, Nature Reviews Physics1, 731 (2019)

    work page 2019

  18. [18]

    G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. Tino, Precision measurement of the newtonian gravitational constant using cold atoms, Nature510, 518 (2014)

    work page 2014

  19. [19]

    Kasevich and S

    M. Kasevich and S. Chu, Atomic interferometry using stimu- lated raman transitions, Physical review letters67, 181 (1991)

    work page 1991

  20. [20]

    C. M. Caves, Quantum-mechanical noise in an interferometer, Phys. Rev. D23, 1693 (1981)

    work page 1981

  21. [21]

    M. Tse, H. Yu, N. Kijbunchoo, A. Fernandez-Galiana, P. Dupej, L. Barsotti, C. Blair, D. Brown, S. e. Dwyer, A. Effler, et al., Quantum-enhanced advanced ligo detectors in the era of gravitational-wave astronomy, Physical Review Letters123, 231107 (2019)

    work page 2019

  22. [22]

    Acernese, M

    F. Acernese, M. Agathos, L. Aiello, A. Allocca, A. Amato, S. Ansoldi, S. Antier, M. Ar `ene, N. Arnaud, S. Ascenzi,et al., Increasing the astrophysical reach of the advanced virgo detec- tor via the application of squeezed vacuum states of light, Phys- ical review letters123, 231108 (2019). 6

    work page 2019

  23. [23]

    Kucsko, P

    G. Kucsko, P. C. Maurer, N. Y . Yao, M. Kubo, H. J. Noh, P. K. Lo, H. Park, and M. D. Lukin, Nanometre-scale thermometry in a living cell, Nature500, 54 (2013)

    work page 2013

  24. [24]

    Dolde, H

    F. Dolde, H. Fedder, M. W. Doherty, T. N ¨obauer, F. Rempp, G. Balasubramanian, T. Wolf, F. Reinhard, L. C. Hollenberg, F. Jelezko,et al., Electric-field sensing using single diamond spins, Nature Physics7, 459 (2011)

    work page 2011

  25. [25]

    J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and R. L. Walsworth, Sensitivity optimization for nv-diamond magnetometry, Reviews of Modern Physics92, 015004 (2020)

    work page 2020

  26. [26]

    H. Zhou, J. Choi, S. Choi, R. Landig, A. M. Douglas, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, P. Cappellaro,et al., Quan- tum metrology with strongly interacting spin systems, Physical review X10, 031003 (2020)

    work page 2020

  27. [27]

    Brida, M

    G. Brida, M. Genovese, and I. Ruo Berchera, Experimental re- alization of sub-shot-noise quantum imaging, Nature Photonics 4, 227 (2010)

    work page 2010

  28. [28]

    Tsang, R

    M. Tsang, R. Nair, and X.-M. Lu, Quantum theory of superres- olution for two incoherent optical point sources, Phys. Rev. X 6, 031033 (2016)

    work page 2016

  29. [29]

    C. A. Casacio, L. S. Madsen, A. Terrasson, M. Waleed, K. Barnscheidt, B. Hage, M. A. Taylor, and W. P. Bowen, Quantum-enhanced nonlinear microscopy, Nature594, 201 (2021)

    work page 2021

  30. [30]

    Cheiney, L

    P. Cheiney, L. Fouch ´e, S. Templier, F. Napolitano, B. Batte- lier, P. Bouyer, and B. Barrett, Navigation-compatible hybrid quantum accelerometer using a kalman filter, Physical Review Applied10, 034030 (2018)

    work page 2018

  31. [31]

    Giovannetti, S

    V . Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett.96, 010401 (2006)

    work page 2006

  32. [32]

    M. G. A. Paris, Quantum estimation for quantum technologies, Int. J. Quantum Inf.07, 125 (2009)

    work page 2009

  33. [33]

    Ticozzi and L

    F. Ticozzi and L. Viola, Quantum resources for purification and cooling: fundamental limits and opportunities, Scientific re- ports4, 5192 (2014)

    work page 2014

  34. [34]

    Demkowicz-Dobrza ´nski, M

    R. Demkowicz-Dobrza ´nski, M. Jarzyna, and J. Kołody ´nski, Chapter four - quantum limits in optical interferometry (Else- vier, 2015) pp. 345–435

    work page 2015

  35. [35]

    Schnabel, Squeezed states of light and their applications in laser interferometers, Phys

    R. Schnabel, Squeezed states of light and their applications in laser interferometers, Phys. Rep.684, 1 (2017)

    work page 2017

  36. [36]

    Pezz `e, A

    L. Pezz `e, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys.90, 035005 (2018)

    work page 2018

  37. [37]

    Pirandola, B

    S. Pirandola, B. R. Bardhan, T. Gehring, C. Weedbrook, and S. Lloyd, Advances in photonic quantum sensing, Nat. Photon- ics12, 724 (2018)

    work page 2018

  38. [38]

    W. Wang, Y . Wu, Y . Ma, W. Cai, L. Hu, X. Mu, Y . Xu, Z.- J. Chen, H. Wang, Y . Song,et al., Heisenberg-limited single- mode quantum metrology in a superconducting circuit, Nature communications10, 4382 (2019)

    work page 2019

  39. [39]

    R. Puig, P. Sekatski, P. A. Erdman, P. Abiuso, J. Calsamiglia, and M. Perarnau-Llobet, From dynamical to steady-state many- body metrology: Precision limits and their attainability with two-body interactions, PRX Quantum6, 030309 (2025)

    work page 2025

  40. [40]

    Fujiwara and H

    A. Fujiwara and H. Imai, A fibre bundle over manifolds of quan- tum channels and its application to quantum statistics, J. Phys. A: Math. Theor.41, 255304 (2008)

    work page 2008

  41. [41]

    Escher, R

    B. Escher, R. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nat. Phys.7, 406 (2011)

    work page 2011

  42. [42]

    Demkowicz-Dobrza ´nski, J

    R. Demkowicz-Dobrza ´nski, J. Kołody´nski, and M. Gut ¸˘a, The elusive heisenberg limit in quantum-enhanced metrology, Nat. Commun.3, 1063 (2012)

    work page 2012

  43. [43]

    Kołody ´nski and R

    J. Kołody ´nski and R. Demkowicz-Dobrza ´nski, Efficient tools for quantum metrology with uncorrelated noise, New J. Phys. 15, 073043 (2013)

    work page 2013

  44. [44]

    S. I. Knysh, E. H. Chen, and G. A. Durkin, True limits to preci- sion via unique quantum probe, arXiv:1402.0495 (2014)

    work page arXiv 2014

  45. [45]

    Demkowicz-Dobrza ´nski and L

    R. Demkowicz-Dobrza ´nski and L. Maccone, Using entangle- ment against noise in quantum metrology, Phys. Rev. Lett.113, 250801 (2014)

    work page 2014

  46. [46]

    Sekatski, M

    P. Sekatski, M. Skotiniotis, J. Kołody ´nski, and W. D ¨ur, Quan- tum metrology with full and fast quantum control, Quantum1, 27 (2017)

    work page 2017

  47. [47]

    Layden, S

    D. Layden, S. Zhou, P. Cappellaro, and L. Jiang, Ancilla-free quantum error correction codes for quantum metrology, Phys. Rev. Lett.122, 040502 (2019)

    work page 2019

  48. [48]

    Zhou and L

    S. Zhou and L. Jiang, Asymptotic theory of quantum channel estimation, PRX Quantum2, 010343 (2021)

    work page 2021

  49. [49]

    Kurdziałek, W

    S. Kurdziałek, W. G ´orecki, F. Albarelli, and R. Demkowicz- Dobrza´nski, Using adaptiveness and causal superpositions against noise in quantum metrology, Phys. Rev. Lett.131, 090801 (2023)

    work page 2023

  50. [50]

    A. Das, W. G ´orecki, and R. Demkowicz-Dobrza´nski, Universal time scalings of sensitivity in markovian quantum metrology, Physical Review A111, L020403 (2025)

    work page 2025

  51. [51]

    G. A. Paz-Silva and L. Viola, General transfer-function ap- proach to noise filtering in open-loop quantum control, Physical review letters113, 250501 (2014)

    work page 2014

  52. [52]

    Viola, E

    L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett.82, 2417 (1999)

    work page 1999

  53. [53]

    T. J. Green, J. Sastrawan, H. Uys, and M. J. Biercuk, Arbitrary quantum control of qubits in the presence of universal noise, New Journal of Physics15, 095004 (2013)

    work page 2013

  54. [54]

    Chen, Geometric continuous dynamical decoupling with bounded controls, Physical Review A—Atomic, Molecular, and Optical Physics73, 022343 (2006)

    P. Chen, Geometric continuous dynamical decoupling with bounded controls, Physical Review A—Atomic, Molecular, and Optical Physics73, 022343 (2006)

    work page 2006

  55. [55]

    Soare, H

    A. Soare, H. Ball, D. Hayes, J. Sastrawan, M. Jarratt, J. McLoughlin, X. Zhen, T. Green, and M. Biercuk, Experi- mental noise filtering by quantum control, Nature Physics10, 825 (2014)

    work page 2014

  56. [56]

    Timoney, I

    N. Timoney, I. Baumgart, M. Johanning, A. Var ´on, M. B. Ple- nio, A. Retzker, and C. Wunderlich, Quantum gates and mem- ory using microwave-dressed states, Nature476, 185 (2011)

    work page 2011

  57. [57]

    X. Xu, Z. Wang, C. Duan, P. Huang, P. Wang, Y . Wang, N. Xu, X. Kong, F. Shi, X. Rong,et al., Coherence-protected quantum gate by continuous dynamical decoupling in diamond, Physical review letters109, 070502 (2012)

    work page 2012

  58. [58]

    D. A. Golter, T. K. Baldwin, and H. Wang, Protecting a solid- state spin from decoherence using dressed spin states, Physical review letters113, 237601 (2014)

    work page 2014

  59. [59]

    Hirose, C

    M. Hirose, C. D. Aiello, and P. Cappellaro, Continuous dynam- ical decoupling magnetometry, Physical Review A—Atomic, Molecular, and Optical Physics86, 062320 (2012)

    work page 2012

  60. [60]

    Arrad, Y

    G. Arrad, Y . Vinkler, D. Aharonov, and A. Retzker, Increasing sensing resolution with error correction, Physical review letters 112, 150801 (2014)

    work page 2014

  61. [61]

    Unden, P

    T. Unden, P. Balasubramanian, D. Louzon, Y . Vinkler, M. B. Plenio, M. Markham, D. Twitchen, A. Stacey, I. Lovchinsky, A. O. Sushkov,et al., Quantum metrology enhanced by repet- itive quantum error correction, Phys. Rev. Lett.116, 230502 (2016)

    work page 2016

  62. [62]

    H. Chen, Y . Chen, J. Liu, Z. Miao, and H. Yuan, Quantum metrology enhanced by leveraging informative noise with error correction, Physical Review Letters133, 190801 (2024)

    work page 2024

  63. [63]

    Demkowicz-Dobrza ´nski, J

    R. Demkowicz-Dobrza ´nski, J. Czajkowski, and P. Sekatski, Adaptive quantum metrology under general markovian noise, 7 Phys. Rev. X7, 041009 (2017)

    work page 2017

  64. [64]

    S. Zhou, M. Zhang, J. Preskill, and L. Jiang, Achieving the heisenberg limit in quantum metrology using quantum error correction, Nat. Commun.9, 78 (2018)

    work page 2018

  65. [65]

    Wan and R

    K. Wan and R. Lasenby, Bounds on adaptive quantum metrol- ogy under markovian noise, Phys. Rev. Res.4, 033092 (2022)

    work page 2022

  66. [66]

    Altherr and Y

    A. Altherr and Y . Yang, Quantum metrology for non-markovian processes, Physical Review Letters127, 060501 (2021)

    work page 2021

  67. [67]

    Kurdziałek, F

    S. Kurdziałek, F. Albarelli, and R. Demkowicz-Dobrza ´nski, Universal bounds for quantum metrology in the presence of cor- related noise, Physical Review Letters135, 130801 (2025)

    work page 2025

  68. [68]

    Z. Mann, N. Cao, R. Laflamme, and S. Zhou, Quantum error- corrected non-markovian metrology, PRX Quantum6, 030321 (2025)

    work page 2025

  69. [69]

    A. W. Chin, S. F. Huelga, and M. B. Plenio, Quantum metrology in non-markovian environments, Phys. Rev. Lett.109, 233601 (2012)

    work page 2012

  70. [70]

    Macieszczak, Zeno limit in frequency estimation with non-markovian environments, Physical Review A92, 010102 (2015)

    K. Macieszczak, Zeno limit in frequency estimation with non-markovian environments, Physical Review A92, 010102 (2015)

    work page 2015

  71. [71]

    Smirne, J

    A. Smirne, J. Kołody ´nski, S. F. Huelga, and R. Demkowicz- Dobrza´nski, Ultimate precision limits for noisy frequency esti- mation, Phys. Rev. Lett.116, 120801 (2016)

    work page 2016

  72. [72]

    J. F. Haase, A. Smirne, J. Kołody ´nski, R. Demkowicz- Dobrza´nski, and S. F. Huelga, Fundamental limits to frequency estimation: a comprehensive microscopic perspective, New Journal of Physics20, 053009 (2018)

    work page 2018

  73. [73]

    Riberi, L

    F. Riberi, L. M. Norris, F. Beaudoin, and L. Viola, Frequency estimation under non-markovian spatially correlated quantum noise, New Journal of Physics24, 103011 (2022)

    work page 2022

  74. [74]

    Riberi and L

    F. Riberi and L. Viola, Optimal asymptotic precision bounds for nonlinear quantum metrology under collective dephasing, APL Quantum2, 10.1063/5.0255629 (2025)

    work page doi:10.1063/5.0255629 2025

  75. [75]

    Riberi, G

    F. Riberi, G. Paz-Silva, and L. Viola, Precision bounds for frequency estimation under collective dephasing and open-loop control, arXiv preprint arXiv:2603.23804 10.48550/arXiv.2603.23804 (2026)

    work page doi:10.48550/arxiv.2603.23804 2026

  76. [76]

    Sekatski, M

    P. Sekatski, M. Skotiniotis, and W. D¨ur, Dynamical decoupling leads to improved scaling in noisy quantum metrology, New Journal of Physics18, 073034 (2016)

    work page 2016

  77. [77]

    Basilewitsch, J

    D. Basilewitsch, J. Fischer, D. M. Reich, D. Sugny, and C. P. Koch, Fundamental bounds on qubit reset, Physical Review Re- search3, 013110 (2021)

    work page 2021

  78. [78]

    Ticozzi and L

    F. Ticozzi and L. Viola, Quantum and classical resources for unitary design of open-system evolutions, Quantum Science and Technology2, 034001 (2017)

    work page 2017

  79. [79]

    Beaudoin, J

    F. Beaudoin, J. M. Gambetta, and A. Blais, Dissipation and ul- trastrong coupling in circuit qed, Physical Review A—Atomic, Molecular, and Optical Physics84, 043832 (2011)

    work page 2011

  80. [80]

    Albash, S

    T. Albash, S. Boixo, D. A. Lidar, and P. Zanardi, Quantum adi- abatic markovian master equations, New Journal of Physics14, 123016 (2012)

    work page 2012

Showing first 80 references.