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arxiv: 2605.18392 · v1 · pith:L2UAZZUGnew · submitted 2026-05-18 · 🪐 quant-ph

Precision limits for time-dependent quantum metrology under Markovian noise

Luca Previdi , Francesco Albarelli This is my paper

Pith reviewed 2026-05-20 11:10 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum metrologyMarkovian noisequantum Fisher informationtime-dependent Hamiltoniansquantum error correctionadaptive protocolsprecision boundsscaling laws
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The pith

Markovian noise limits the long-time QFI scaling for time-dependent parameters to at most T to the 2k or T to the 2k-1 depending on the regime.

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

The paper derives ultimate precision bounds for estimating parameters encoded in time-dependent Hamiltonians in the presence of general Markovian noise, allowing arbitrary adaptive protocols with fast controls and noiseless ancillas. It extends the minimization-over-purifications framework to time-varying continuous channels to obtain a differential upper bound on the quantum Fisher information, which can be evaluated at all times via semidefinite programming. For parameter-independent noise, the work proves a universal scaling law: if the coherent dynamics yields QFI scaling as T to the power 2k, then the noisy case is bounded by T to the 2k in the DHNLS regime but only T to the 2k-1 in the DHLS regime. These limits are illustrated on driven-qubit sensors and shown to be tight through explicit quantum error correction constructions supplemented by spin-squeezed probes.

Core claim

When the noiseless coherent dynamics produces Q_coh(T) scaling as T to the 2k, Markovian noise restricts the achievable QFI to at most T to the 2k in the DHNLS regime and fundamentally to T to the 2k-1 in the DHLS regime for parameter-independent noise. This holds for arbitrary adaptive protocols and is saturated asymptotically by continuous quantum error correction codes.

What carries the argument

The minimization-over-purifications framework extended to time-varying continuous channels, which produces a computable differential upper bound on the QFI that is evaluated via semidefinite programming.

If this is right

  • Driven-qubit sensors can reach T to the 4 scaling under dephasing noise and T to the 3 under spontaneous emission when protocols respect the derived bounds.
  • Continuous quantum error correction combined with spin squeezing can asymptotically achieve the ultimate scaling in both regimes.
  • The differential bound permits computation of the achievable precision at every intermediate time, not only in the long-time limit.
  • The scaling law applies uniformly to any time-dependent Hamiltonian encoding as long as the noise is Markovian and parameter-independent.

Where Pith is reading between the lines

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

  • Selecting or engineering the noise channel toward the DHNLS regime could preserve higher scaling without changing the underlying coherent drive.
  • The same differential bound technique might be adapted to analyze non-Markovian or discrete-time noise if a suitable purification minimization can be formulated.
  • In experimental settings, the SDP-evaluable bound offers a practical benchmark for testing whether a given sensor protocol is operating near the fundamental limit.
  • Combining the scaling results with existing work on time-independent metrology could yield hybrid protocols that switch regimes dynamically.

Load-bearing premise

The minimization-over-purifications approach extends rigorously to time-varying continuous quantum channels and supplies a valid upper bound for arbitrary adaptive protocols.

What would settle it

Observing a QFI that grows faster than T to the 2k-1 over long times in the DHLS regime for a parameter-independent Markovian noise process would contradict the claimed scaling law.

Figures

Figures reproduced from arXiv: 2605.18392 by Francesco Albarelli, Luca Previdi.

Figure 1
Figure 1. Figure 1: FIG. 1. Pictorial representation of the most general [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Plot of the full numerically optimized bound [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. a) Pictorial representation of the QEC scheme [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

We derive ultimate precision bounds for estimating parameters encoded in \emph{time-dependent} Hamiltonians in the presence of general Markovian noise, allowing for arbitrary adaptive protocols with fast controls and noiseless ancillas. Extending the minimization-over-purifications framework to time-varying continuous channels, we obtain a differential upper bound on the achievable quantum Fisher information (QFI) that can be evaluated at all times via semidefinite programming. For parameter-independent noise, we prove a universal long-time scaling law: if the coherent (noiseless) dynamics yields $Q_{\mathrm{coh}}(T)\sim T^{2k}$, then under Markovian noise the QFI scales at most as $Q(T)\sim T^{2k}$ in the DHNLS regime, whereas in the DHLS regime it is fundamentally limited to $Q(T)\sim T^{2k-1}$. We illustrate these behaviors on paradigmatic driven-qubit sensors, exhibiting $T^{4}$ and $T^{3}$ scalings under dephasing and spontaneous emission, respectively. Finally, we provide explicit continuous exact and approximate quantum error correction constructions -- supplemented by spin-squeezed probes -- that asymptotically saturate the bounds, establishing their tightness.

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

1 major / 2 minor

Summary. The paper derives ultimate precision bounds for estimating parameters encoded in time-dependent Hamiltonians under general Markovian noise, allowing arbitrary adaptive protocols with fast controls and noiseless ancillas. It extends the minimization-over-purifications framework to time-varying continuous channels to obtain a differential upper bound on the quantum Fisher information (QFI) evaluable via semidefinite programming at all times. For parameter-independent noise, it proves a universal long-time scaling law: if the coherent dynamics yields Q_coh(T)∼T^{2k}, then under noise the QFI scales at most as Q(T)∼T^{2k} in the DHNLS regime and is limited to Q(T)∼T^{2k-1} in the DHLS regime. The claims are illustrated with driven-qubit sensors showing T^4 and T^3 scalings and supported by explicit continuous quantum error correction constructions (with spin-squeezed probes) that asymptotically saturate the bounds.

Significance. If the central derivation holds, the work provides valuable general, computable bounds and asymptotic scaling laws for adaptive time-dependent quantum metrology under Markovian noise, filling a gap relative to prior time-independent analyses. The SDP-based differential bound and the explicit saturating constructions (including QEC) are strengths that make the results falsifiable and potentially useful for sensor design. The universal scaling claim, if rigorously established, would be a notable contribution to the field.

major comments (1)
  1. [derivation of the differential upper bound] The extension of the minimization-over-purifications method to time-varying continuous channels (as outlined after the abstract and in the main derivation) is load-bearing for the differential QFI upper bound and the subsequent scaling laws. The manuscript should explicitly address whether the instantaneous SDP fully captures cross terms between the time-dependent control Hamiltonian and noise operators under arbitrary fast adaptive controls, to confirm that no additional scaling is possible in the DHLS regime beyond the stated T^{2k-1} limit.
minor comments (2)
  1. [abstract and introduction] The acronyms DHNLS and DHLS are used in the scaling law statement but should be defined at first use or in a dedicated notation table for clarity.
  2. [examples section] The illustrative examples on driven-qubit sensors would benefit from a brief comparison table showing the achieved scalings versus the derived bounds.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comment on the derivation of the differential upper bound. We appreciate the positive assessment of the work's significance and the recognition of the SDP-based bound and saturating constructions. We address the major comment below and have revised the manuscript to provide the requested clarification.

read point-by-point responses

  1. Referee: [derivation of the differential upper bound] The extension of the minimization-over-purifications method to time-varying continuous channels (as outlined after the abstract and in the main derivation) is load-bearing for the differential QFI upper bound and the subsequent scaling laws. The manuscript should explicitly address whether the instantaneous SDP fully captures cross terms between the time-dependent control Hamiltonian and noise operators under arbitrary fast adaptive controls, to confirm that no additional scaling is possible in the DHLS regime beyond the stated T^{2k-1} limit.

    Authors: We thank the referee for raising this important point regarding the generality of the bound. In the derivation, the time-dependent channel is treated via its infinitesimal generator, which incorporates the full time-dependent control Hamiltonian H(t) together with the Markovian noise operators into a single effective Liouvillian. The minimization over purifications is performed on this complete generator at each instant, and the resulting SDP is optimized over all possible purifications of the joint system-environment evolution. This procedure explicitly accounts for any cross terms arising from the commutation or anticommutation relations between H(t) and the noise operators, as well as for arbitrary fast adaptive controls (including those that depend on prior measurement outcomes). Consequently, the instantaneous bound already encompasses the most general adaptive strategies permitted by Markovian dynamics, and no additional scaling beyond T^{2k-1} is possible in the DHLS regime. To make this explicit, we have added a new explanatory paragraph immediately following the statement of the differential bound (in the section deriving the SDP), together with a brief remark on the inclusion of control-noise cross terms. We believe this revision addresses the referee's concern without altering the technical claims. revision: yes

Circularity Check

0 steps flagged

Derivation of QFI bounds and scaling laws is self-contained

full rationale

The paper extends the minimization-over-purifications framework to time-varying continuous channels to obtain a differential upper bound on QFI evaluable via SDP for arbitrary adaptive protocols. From this bound it derives the long-time scaling laws (Q(T)∼T^{2k} in DHNLS, ∼T^{2k-1} in DHLS) for parameter-independent noise when the coherent case scales as T^{2k}. No step reduces by construction to a fitted parameter renamed as prediction, a self-definitional loop, or a load-bearing self-citation whose content is itself unverified; the scaling follows from integrating the differential bound under the stated regimes. The constructions that saturate the bounds are presented as explicit and independent, confirming the derivation does not collapse to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of extending the minimization-over-purifications framework to time-dependent Markovian channels and on the Markovian noise model itself.

axioms (1)
  • domain assumption Noise is Markovian and parameter-independent
    Invoked to derive the universal long-time scaling law and to allow the differential QFI bound.

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Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 22 internal anchors

  1. [1]

    C. W. Helstrom,Quantum Detection and Estima- tion Theory(Academic Press, New York, 1976)

    work page 1976

  2. [2]

    W. K. Wootters, Statistical distance and Hilbert space, Phys. Rev. D23, 357 (1981)

    work page 1981

  3. [3]

    S. L. Braunstein and C. M. Caves, Statistical dis- tance and the geometry of quantum states, Phys. Rev. Lett.72, 3439 (1994)

    work page 1994

  4. [4]

    S. L. Braunstein, C. M. Caves, and G. J. Milburn, Generalized Uncertainty Relations: Theory, Exam- 6 ples, and Lorentz Invariance, Ann. Phys.247, 135 (1996), arXiv:quant-ph/9507004

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  5. [5]

    M. G. A. Paris, Quantum estimation for quantum technology, Int. J. Quantum Inf.07, 125 (2009), arXiv:0804.2981

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  6. [6]

    Quantum limits in optical interferometry

    R. Demkowicz-Dobrza´ nski, M. Jarzyna, and J. Ko/suppress lody´ nski, Quantum Limits in Optical Interfer- ometry, inProgress in Optics, Volume 60, edited by E. Wolf (Elsevier, Amsterdam, 2015) pp. 345–435, arXiv:1405.7703

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  7. [7]

    M. J. Holland and K. Burnett, Interferometric de- tection of optical phase shifts at the Heisenberg limit, Phys. Rev. Lett.71, 1355 (1993)

    work page 1993

  8. [8]

    Quantum-enhanced measurements: beating the standard quantum limit

    V. Giovannetti, S. Lloyd, and L. Maccone, Quantum-Enhanced Measurements: Beating the Standard Quantum Limit, Science306, 1330 (2004), arXiv:quant-ph/0412078

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  9. [9]

    Giovannetti, S

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

    work page 2006

  10. [10]

    Advances in Quantum Metrology

    V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics5, 222 (2011), arXiv:1102.2318v1

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  11. [11]

    T. L. S. Collaboration, A gravitational wave obser- vatory operating beyond the quantum shot-noise limit, Nat. Phys.7, 962 (2011), arXiv:1109.2295

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  12. [12]

    Y. A. Yang, M. Miklos, Y. M. Tso, S. Kraus, J. Hur, and J. Ye, Clock Precision beyond the Standard Quantum Limit at$ {10}ˆ{\ensuremath{- }18}$Level, Phys. Rev. Lett.135, 193202 (2025)

    work page 2025

  13. [13]

    I. K. Kominis, Sub-Shot-Noise Magnetometry with a Correlated Spin-Relaxation Dominated Alkali- Metal Vapor, Phys. Rev. Lett.100, 073002 (2008), arXiv:0708.0330

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  14. [14]

    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 magne- tometry, Rev. Mod. Phys.92, 015004 (2020), arXiv:1903.08176

    work page arXiv 2020

  15. [15]

    Gorini, A

    V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N- level systems, J. Math. Phys.17, 821 (1976)

    work page 1976

  16. [16]

    On the long-time asymptotics of quantum dynamical semigroups

    G. Lindblad, On the generators of quantum dynam- ical semigroups, Commun. Math. Phys.48, 119 (1976), arXiv:1402.7287v1

    work page internal anchor Pith review Pith/arXiv arXiv 1976

  17. [17]

    B. M. Escher, R. L. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum- enhanced metrology, Nat. Phys.7, 406 (2011), arXiv:1201.1693

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  18. [18]

    The elusive Heisenberg limit in quantum enhanced metrology

    R. Demkowicz-Dobrza´ nski, J. Ko/suppress lody´ nski, and M. Gu t ¸˘ a, The elusive Heisenberg limit in quantum- enhanced metrology, Nat. Commun.3, 1063 (2012), arXiv:1201.3940

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  19. [19]

    Using entanglement against noise in quantum metrology

    R. Demkowicz-Dobrza´ nski and L. Maccone, Us- ing Entanglement Against Noise in Quantum Metrology, Phys. Rev. Lett.113, 250801 (2014), arXiv:1407.2934

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  20. [20]

    Quantum metrology with full and fast quantum control

    P. Sekatski, M. Skotiniotis, J. Ko/suppress lody´ nski, and W. D¨ ur, Quantum metrology with full and fast quantum control, Quantum1, 27 (2017), arXiv:1603.08944

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  21. [21]

    Adaptive quantum metrology under general Markovian noise

    R. Demkowicz-Dobrza´ nski, J. Czajkowski, and P. Sekatski, Adaptive Quantum Metrology under General Markovian Noise, Phys. Rev. X7, 041009 (2017), arXiv:1704.06280

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  22. [22]

    S. Zhou, M. Zhang, J. Preskill, and L. Jiang, Achiev- ing the Heisenberg limit in quantum metrology us- ing quantum error correction, Nat. Commun.9, 78 (2018), arXiv:1706.02445

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  23. [23]

    Wan and R

    K. Wan and R. Lasenby, Bounds on adaptive quan- tum metrology under Markovian noise, Phys. Rev. Research4, 033092 (2022), arXiv:2108.11390

    work page arXiv 2022

  24. [24]

    Kurdzia/suppress lek, W

    S. Kurdzia/suppress lek, 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), arXiv:2212.08106

    work page arXiv 2023

  25. [25]

    Z. Mann, N. Cao, R. Laflamme, and S. Zhou, Quan- tum Error-Corrected Non-Markovian Metrology, PRX Quantum6, 030321 (2025), arXiv:2503.07745

    work page arXiv 2025

  26. [26]

    Protecting Heisenberg scaling in quantum metrology via engineered dressed states

    W. Gorecki and C. P. Koch, Protecting Heisen- berg scaling in quantum metrology via engineered dressed states (2026), arXiv:2604.14098

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  27. [27]

    Zhou and L

    S. Zhou and L. Jiang, Optimal approximate quan- tum error correction for quantum metrology, Phys. Rev. Res.2, 013235 (2020), arXiv:1910.08472

    work page arXiv 2020

  28. [28]

    Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

    S. Pang and A. N. Jordan, Optimal adaptive con- trol for quantum metrology with time-dependent Hamiltonians, Nat. Commun.8, 14695 (2017), arXiv:1606.02166

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  29. [29]

    J. Yang, S. Pang, and A. N. Jordan, Quan- tum parameter estimation with the Landau-Zener transition, Phys. Rev. A96, 020301 (2017), arXiv:1612.02390

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  30. [30]

    Control methods for improved Fisher information with quantum sensing

    T. Gefen, F. Jelezko, and A. Retzker, Control meth- ods for improved Fisher information with quan- tum sensing, Phys. Rev. A96, 032310 (2017), arXiv:1702.07408

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  31. [31]

    Achieving optimal quantum acceleration of frequency estimation using adaptive coherent control

    M. Naghiloo, A. N. Jordan, and K. W. Murch, Achieving Optimal Quantum Acceleration of Fre- quency Estimation Using Adaptive Coherent Control, Phys. Rev. Lett.119, 180801 (2017), arXiv:1706.05649

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  32. [32]

    Gefen, A

    T. Gefen, A. Rotem, and A. Retzker, Overcom- ing resolution limits with quantum sensing, Nat. Commun.10, 4992 (2019), arXiv:1811.01762

    work page arXiv 2019

  33. [33]

    Sub-millihertz magnetic spectroscopy with a nanoscale quantum sensor

    S. Schmitt, T. Gefen, F. M. St¨ urner, T. Unden, G. Wolff, C. R. M¨ uller, J. Scheuer, B. Naydenov, M. Markham, S. Pezzagna, J. Meijer, I. Schwarz, M. B. Plenio, A. Retzker, L. P. McGuinness, and F. Jelezko, Submillihertz magnetic spectroscopy per- formed with a nanoscale quantum sensor, Science 356, 832 (2017), arXiv:1706.02103

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  34. [34]

    Meinel, V

    J. Meinel, V. Vorobyov, P. Wang, B. Yavkin, M. Pfender, H. Sumiya, S. Onoda, J. Isoya, R.-B. Liu, and J. Wrachtrup, Quantum nonlinear spec- troscopy of single nuclear spins, Nat Commun13, 5318 (2022), arXiv:2109.11170

    work page arXiv 2022

  35. [35]

    Gribben, A

    D. Gribben, A. Sanpera, R. Fazio, J. Marino, and F. Iemini, Boundary time crystals as AC sensors: Enhancements and constraints, SciPost Phys.18, 100 (2025), arXiv:2406.06273

    work page arXiv 2025

  36. [36]

    A. M. Polloreno, J. L. Beckey, J. Levin, A. Shlos- berg, J. K. Thompson, M. Foss-Feig, D. Hayes, and G. Smith, Opportunities and Limitations in Broad- band Sensing, Phys. Rev. Appl.19, 014029 (2023), arXiv:2203.05520

    work page arXiv 2023

  37. [37]

    R. R. Allen, F. Machado, I. L. Chuang, H.-Y. Huang, and S. Choi, Quantum Computing En- hanced Sensing (2025), arXiv:2501.07625

    work page arXiv 2025

  38. [38]

    A. Dey, S. Mouradian, C. Lupo, and Z. Huang, Quantum-Optimal Frequency Estimation of Stochastic ac Fields, Phys. Rev. Lett.135, 130802 (2025), arXiv:2411.19412. 7

    work page arXiv 2025

  39. [39]

    A. M. Polloreno and G. Smith, Simple broadband signal detection at the fundamental limit (2026), arXiv:2601.19816

    work page arXiv 2026

  40. [40]

    Fujiwara and H

    A. Fujiwara and H. Imai, A fibre bundle over man- ifolds of quantum channels and its application to quantum statistics, J. Phys. A41, 255304 (2008)

    work page 2008

  41. [41]

    A. Das, W. G´ orecki, and R. Demkowicz-Dobrza´ nski, Universal time scalings of sensitivity in Markovian quantum metrology, Phys. Rev. A111, L020403 (2025), arXiv:2404.03954

    work page arXiv 2025

  42. [42]

    Ulam-Orgikh and M

    D. Ulam-Orgikh and M. Kitagawa, Spin squeez- ing and decoherence limit in Ramsey spectroscopy, Phys. Rev. A64, 052106 (2001)

    work page 2001

  43. [43]

    Zhou,Error-Corrected Quantum Metrology, Ph.D

    S. Zhou,Error-Corrected Quantum Metrology, Ph.D. thesis, Yale University (2021)

    work page 2021

  44. [44]

    Efficient tools for quantum metrology with uncorrelated noise

    J. Ko/suppress lody´ nski and R. Demkowicz-Dobrza´ nski, Ef- ficient tools for quantum metrology with uncor- related noise, New J. Phys.15, 073043 (2013), arXiv:1303.7271

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  45. [45]

    Supplemental Material

    work page

  46. [46]

    S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Improvement of Frequency Standards with Quantum Entanglement, Phys. Rev. Lett.79, 3865 (1997), arXiv:quant- ph/9707014

    work page arXiv 1997

  47. [47]

    Super-Heisenberg

    Z. Hou, Y. Jin, H. Chen, J.-F. Tang, C.-J. Huang, H. Yuan, G.-Y. Xiang, C.-F. Li, and G.-C. Guo, “Super-Heisenberg” and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Ro- tating Field, Phys. Rev. Lett.126, 070503 (2021)

    work page 2021

  48. [48]

    Here small is intended with respect to the system energy scales but not small enough to break the Lindblad representation

    work page

  49. [49]

    S. Zhou, A. G. Manes, and L. Jiang, Achieving metrological limits using ancilla-free quantum error- correcting codes, Phys. Rev. A109, 042406 (2024), arXiv:2303.00881

    work page arXiv 2024

  50. [50]

    H. Sahu, Q. Xu, and S. Zhou, Achieving the Heisen- berg limit using fault-tolerant quantum error cor- rection (2026), arXiv:2601.05457

    work page arXiv 2026

  51. [51]

    Y. Chen, Z. Wang, and S. Zhou, Quantum metrol- ogy via partial quantum error correction (2026), arXiv:2605.08341

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  52. [52]

    Kurdzia/suppress lek, F

    S. Kurdzia/suppress lek, F. Albarelli, and R. Demkowicz- Dobrza´ nski, Universal Bounds for Quantum Metrol- ogy in the Presence of Correlated Noise, Phys. Rev. Lett.135, 130801 (2025), arXiv:2410.01881

    work page arXiv 2025