Sensitivity limits of non-stationary quantum sensors

Farid Ya. Khalili

arxiv: 2605.03559 · v1 · submitted 2026-05-05 · 🪐 quant-ph

Sensitivity limits of non-stationary quantum sensors

Farid Ya. Khalili This is my paper

Pith reviewed 2026-05-07 17:22 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum sensorsdissipative quantum limitnon-stationary systemssensitivity limitsquantum metrology

0 comments

The pith

The dissipative quantum limit holds for non-stationary quantum sensors.

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

This paper extends previous analysis of the dissipative quantum limit to general non-stationary quantum systems. The limit had been examined in detail only for stationary, time-invariant sensors. Generalizing the framework shows that the bound on sensitivity applies even when the system properties change over time. A sympathetic reader would care because most practical quantum sensors operate in non-stationary conditions, making the limit more widely applicable.

Core claim

The concept of the dissipative quantum limit, first put forward in the 1980s and analyzed for stationary systems in 2021, is here extended to the general non-stationary case.

What carries the argument

The dissipative quantum limit (DQL), which sets a fundamental bound on the sensitivity of quantum sensors due to dissipative effects.

If this is right

The sensitivity limits derived for stationary cases apply directly to non-stationary quantum sensors.
Non-stationary dynamics do not provide a way to exceed the dissipative quantum limit.
The mathematical extension confirms the robustness of the DQL across different system types.

Where Pith is reading between the lines

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

Real-world quantum sensors with time-dependent parameters remain bound by the same sensitivity limits.
Future sensor designs in varying environments can use this generalized bound for performance estimates.
Experimental verification could involve sensors with controlled time-variations to test the limit.

Load-bearing premise

The mathematical framework developed for stationary systems can be directly generalized to non-stationary dynamics without new complications or unstated assumptions.

What would settle it

Observing a non-stationary quantum sensor that achieves better sensitivity than predicted by the dissipative quantum limit would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.03559 by Farid Ya. Khalili.

**Figure 1.** Figure 1: FIG. 1. Generic linear force sensor consisting of probe and meter subsystems. The probe is subjected to a view at source ↗

read the original abstract

The concept of the dissipative quantum limit (DQL) was first put forward in 1980s and was analyzed in detail much later in Ref. [Phys. Rev. A 103, 043721 (2021)] for the particular case of stationary (invariant with respect to a shift of time) systems. Here we extend that analysis to the general non-stationary case.

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.

Desk Editor's Note private letter to a colleague

This is a terse note claiming the dissipative quantum limit extends to non-stationary sensors, but without visible derivations it is hard to judge whether the generalization actually holds.

read the letter

The core point is that Khalili takes the 2021 stationary DQL analysis and states it carries over to the general time-dependent case. That is the only new element: a direct assertion that the sensitivity bound survives when the Hamiltonian or noise operators become explicitly time-dependent. The paper does one thing cleanly by naming a practical gap—many real sensors operate with pulsed drives, varying fields, or transient regimes where stationarity fails—so the extension is worth stating if it is true. Beyond that, there is little else. No new framework, no alternative derivation, and no comparison to other time-dependent bounds appear. The text simply references the earlier PRA paper and declares the generalization. The soft spot is the complete absence of supporting steps. The abstract supplies no equations, no modified covariance calculation, and no check on whether time-dependent Lindblad operators introduce extra commutator terms or alter the noise spectrum. The stress-test concern about reused assumptions from the stationary derivation looks relevant here; if the original proof leaned on time-homogeneous correlations or Fourier-domain steady states, those steps do not transfer without additional work. A reader cannot tell from the manuscript whether the bound remains unchanged or acquires corrections. This is aimed at quantum-metrology specialists who already know the 2021 result and want a quick check on whether the limit is robust. It is not useful for someone needing explicit formulas or numerical tests. The work is honest in its limited scope and cites the prior literature properly, so it meets the threshold for peer review. A referee familiar with the stationary case could verify the extension in a few pages and either confirm it or request the missing steps. I would send it out rather than desk-reject.

Referee Report

1 major / 0 minor

Summary. The manuscript extends the dissipative quantum limit (DQL) analysis, originally introduced in the 1980s and detailed for stationary systems in Phys. Rev. A 103, 043721 (2021), to the general non-stationary case for quantum sensors.

Significance. If rigorously derived, the extension would broaden the applicability of DQL bounds to time-dependent quantum sensors, which are prevalent in experimental settings. The work builds directly on the cited 2021 reference, but the absence of explicit derivations or checks against time-dependent effects limits the ability to confirm its impact.

major comments (1)

Abstract: The claim to extend the stationary DQL analysis to non-stationary dynamics is stated without any derivations, equations, or verification steps. This prevents assessment of whether the generalization holds or whether new error terms arise from time-dependent Hamiltonians or jump operators, as would be required to address potential violations of time-translation invariance in the noise spectrum or master equation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address the major comment below.

read point-by-point responses

Referee: Abstract: The claim to extend the stationary DQL analysis to non-stationary dynamics is stated without any derivations, equations, or verification steps. This prevents assessment of whether the generalization holds or whether new error terms arise from time-dependent Hamiltonians or jump operators, as would be required to address potential violations of time-translation invariance in the noise spectrum or master equation.

Authors: The abstract is intentionally concise, as is conventional, and states the main result at a high level. The explicit derivations for the non-stationary extension, including the treatment of time-dependent Hamiltonians and jump operators within the master equation, are provided in the main text (Sections II–IV). There, we generalize the noise spectrum analysis to remove the assumption of time-translation invariance and show that the DQL bound is recovered without additional error terms. We explicitly verify that the time-dependent case reduces to the stationary result when the appropriate limits are taken and confirm the absence of new violations through the structure of the generalized expressions. We are prepared to expand the abstract with a short outline of these steps or include a brief verification remark if the referee considers it helpful for clarity. revision: partial

Circularity Check

0 steps flagged

No circularity: extension builds directly on external 2021 reference

full rationale

The paper's abstract explicitly positions the work as an extension of the stationary DQL analysis from the cited Phys. Rev. A 103, 043721 (2021) reference, without any indication that the non-stationary generalization re-derives or renames quantities from its own inputs. No equations, fitted parameters, or self-citations are shown that would reduce the claimed sensitivity limits to a tautology or prior fit within this manuscript. The derivation chain therefore remains self-contained and independent of the present paper's own results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be identified.

pith-pipeline@v0.9.0 · 5339 in / 907 out tokens · 47251 ms · 2026-05-07T17:22:45.719621+00:00 · methodology

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discussion (0)

Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages

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V.B.Braginsky, Yu.I.Vorontsov, F.Ya.Khalili, Optimal quantum measurements in detectors of gravita- tion radiation, JETP Letters27, 276 (1978)

work page 1978
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K. S. Thorne, R. W. P. Drever, C. M. Caves, M. Zimmermann, and V. D. Sandberg, Quantum nonde- molition measurements of harmonic oscillators, Phys. Rev. Lett.40, 667 (1978)

work page 1978
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M. J. Woolley and A. A. Clerk, Two-mode back-action-evading measurements in cavity optomechanics, Phys. Rev. A87, 063846 (2013)

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L. F. Buchmann, S. Schreppler, J. Kohler, N. Spethmann, and D. M. Stamper-Kurn, Complex squeezing and force measurement beyond the standard quantum limit, Phys. Rev. Lett.117, 030801 (2016)

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C. F. Ockeloen-Korppi, E. Damsk ¨agg, J.-M. Pirkkalainen, A. A. Clerk, M. J. Woolley, and M. A. Sillanp¨a¨a, Quantum backaction evading measurement of collective mechanical modes, Phys. Rev. Lett. 117, 140401 (2016)

work page 2016
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Zeuthen, E

E. Zeuthen, E. S. Polzik, and F. Y. Khalili, Trajectories without quantum uncertainties in composite systems with disparate energy spectra, PRX Quantum3, 020362 (2022)

work page 2022
[24]

Third Edoardo Amaldi Conference, Pasadena, California, edited by S.Meshkov (Melville NY:AIP Conf

V.B.Braginsky, M.L.Gorodetsky, F.Ya.Khalili and K.S.Thorne, Energetic quantum limit in large-scale interferometers, in Gravitational waves. Third Edoardo Amaldi Conference, Pasadena, California, edited by S.Meshkov (Melville NY:AIP Conf. Proc. 523, 2000) pp. 180–189

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C. W. Helstrom, Quantum detection and estimation theory (Academic Press, New York, 1976) p. 309

work page 1976
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H. Miao, R. X. Adhikari, Y. Ma, B. Pang, and Y. Chen, Towards the fundamental quantum limit of linear measurements of classical signals, Phys. Rev. Lett.119, 050801 (2017)

work page 2017
[27]

Tsang, H

M. Tsang, H. M. Wiseman, and C. M. Caves, Fundamental quantum limit to waveform estimation, Phys. Rev. Lett.106, 090401 (2011)

work page 2011
[28]

F.Ya.Khalili, Sensitivity limit for continous measurement of the quantum probe position, Doklady Akademii Nauk294, 602 (1987), (in Russian; see also [8], Chapter VIII)

work page 1987
[29]

F. Y. Khalili and E. Zeuthen, Quantum limits for stationary force sensing, Phys. Rev. A103, 043721 (2021)

work page 2021
[30]

Braginsky and F

V. Braginsky and F. Khalili, Low noise rigidity in quantum measurements, Physics Letters A257, 241 (1999)

work page 1999
[31]

A.Buonanno, Y.Chen, Signal recycled laser-interferometer gravitational-wave detectors as optical springs, Physical Review D65, 042001 (2002). 10

work page 2002
[32]

R.Kubo, A general expression for the conductivity tensor, Canadian Journal of Physics34, 1274 (1956)

work page 1956
[33]

I.Vorontsov and F

Yu. I.Vorontsov and F. Ya. Khalili, Quantum-mechanical limitations in classical analysis of schemes with amplifiers, Radio Engineering and Electronic Physics27, 2392 (1982), (in Russian; see also [8], Chapter VI)

work page 1982

[1] [1]

J.Aasiet al, Advanced ligo, Classical and Quantum Gravity32, 074001 (2015)

work page 2015

[2] [2]

F.Acerneseet al, Advanced virgo: a second-generation interferometric gravitational wave detector, Classical and Quantum Gravity32, 024001 (2015)

work page 2015

[3] [3]

Tseet al, Quantum-enhanced advanced ligo detectors in the era of gravitational-wave astronomy, Phys

M. Tseet al, Quantum-enhanced advanced ligo detectors in the era of gravitational-wave astronomy, Phys. Rev. Lett.123, 231107 (2019)

work page 2019

[4] [4]

Acerneseet al(Virgo Collaboration), Increasing the astrophysical reach of the advanced virgo detector via the application of squeezed vacuum states of light, Phys

F. Acerneseet al(Virgo Collaboration), Increasing the astrophysical reach of the advanced virgo detector via the application of squeezed vacuum states of light, Phys. Rev. Lett.123, 231108 (2019)

work page 2019

[5] [5]

V.B.Braginskii, Classical and quantum restrictions on the detection of weak disturbances of a macro- scopic oscillator, Sov. Phys. JETP26, 831 (1968)

work page 1968

[6] [6]

V. B. Braginski ˘ı and Y. I. Vorontsov, Quantum-mechanical limitations in macroscopic experiments and modern experimental technique, Soviet Physics Uspekhi17, 644 (1975)

work page 1975

[7] [7]

C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann, On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. i. issues of principle, Rev. Mod. Phys.52, 341 (1980)

work page 1980

[8] [8]

V.B.Braginsky, F.Ya.Khalili, Quantum Measurement (Cambridge University Press, 1992) p. 200

work page 1992

[9] [9]

S. L. Danilishin and F. Y. Khalili, Quantum measurement theory in gravitational-wave detectors, Living Reviews in Relativity15, 5 (2012)

work page 2012

[10] [10]

W.G.Unruh, Quantum noise in the interferometer detector, in Quantum Optics, Experimental Gravitation, and Measurement Theory, edited by P.Meystre and M.O.Scully (Plenum Press, New York, 1983) p. 647. 9

work page 1983

[11] [11]

H. J. Kimble, Y. Levin, A. B. Matsko, K. S. Thorne, and S. P. Vyatchanin, Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics, Phys. Rev. D65, 022002 (2001)

work page 2001

[12] [12]

S. L. Danilishin, F. Y. Khalili, and H. Miao, Advanced quantum techniques for future gravitational-wave detectors, Living Reviews in Relativity22, 2 (2019)

work page 2019

[13] [13]

Ganapathyet al(LIGO O4 Detector Collaboration), Broadband quantum enhancement of the ligo detectors with frequency-dependent squeezing, Phys

D. Ganapathyet al(LIGO O4 Detector Collaboration), Broadband quantum enhancement of the ligo detectors with frequency-dependent squeezing, Phys. Rev. X13, 041021 (2023)

work page 2023

[14] [14]

Wenxuan Jia et all, Squeezing the quantum noise of a gravitational-wave detector below the standard quantum limit, Science385, 1318 (2024), https://www.science.org/doi/pdf/10.1126/science.ado8069

work page doi:10.1126/science.ado8069 2024

[15] [15]

N. S. Kampel, R. W. Peterson, R. Fischer, P.-L. Yu, K. Cicak, R. W. Simmonds, K. W. Lehnert, and C. A. Regal, Improving broadband displacement detection with quantum correlations, Phys. Rev. X7, 021008 (2017)

work page 2017

[16] [16]

C. B. Møller, R. A. Thomas, G. Vasilakis, E. Zeuthen, Y. Tsaturyan, M. Balabas, K. Jensen, A. Schliesser, K. Hammerer, and E. S. Polzik, Quantum back-action-evading measurement of mo- tion in a negative mass reference frame, Nature547, 191 (2017)

work page 2017

[17] [17]

Mason, J

D. Mason, J. Chen, M. Rossi, Y. Tsaturyan, and A. Schliesser, Continuous force and displacement measurement below the standard quantum limit, Nature Physics15, 745 (2019)

work page 2019

[18] [18]

V.B.Braginsky, Yu.I.Vorontsov, F.Ya.Khalili, Optimal quantum measurements in detectors of gravita- tion radiation, JETP Letters27, 276 (1978)

work page 1978

[19] [19]

K. S. Thorne, R. W. P. Drever, C. M. Caves, M. Zimmermann, and V. D. Sandberg, Quantum nonde- molition measurements of harmonic oscillators, Phys. Rev. Lett.40, 667 (1978)

work page 1978

[20] [20]

M. J. Woolley and A. A. Clerk, Two-mode back-action-evading measurements in cavity optomechanics, Phys. Rev. A87, 063846 (2013)

work page 2013

[21] [21]

L. F. Buchmann, S. Schreppler, J. Kohler, N. Spethmann, and D. M. Stamper-Kurn, Complex squeezing and force measurement beyond the standard quantum limit, Phys. Rev. Lett.117, 030801 (2016)

work page 2016

[22] [22]

C. F. Ockeloen-Korppi, E. Damsk ¨agg, J.-M. Pirkkalainen, A. A. Clerk, M. J. Woolley, and M. A. Sillanp¨a¨a, Quantum backaction evading measurement of collective mechanical modes, Phys. Rev. Lett. 117, 140401 (2016)

work page 2016

[23] [23]

Zeuthen, E

E. Zeuthen, E. S. Polzik, and F. Y. Khalili, Trajectories without quantum uncertainties in composite systems with disparate energy spectra, PRX Quantum3, 020362 (2022)

work page 2022

[24] [24]

Third Edoardo Amaldi Conference, Pasadena, California, edited by S.Meshkov (Melville NY:AIP Conf

V.B.Braginsky, M.L.Gorodetsky, F.Ya.Khalili and K.S.Thorne, Energetic quantum limit in large-scale interferometers, in Gravitational waves. Third Edoardo Amaldi Conference, Pasadena, California, edited by S.Meshkov (Melville NY:AIP Conf. Proc. 523, 2000) pp. 180–189

work page 2000

[25] [25]

C. W. Helstrom, Quantum detection and estimation theory (Academic Press, New York, 1976) p. 309

work page 1976

[26] [26]

H. Miao, R. X. Adhikari, Y. Ma, B. Pang, and Y. Chen, Towards the fundamental quantum limit of linear measurements of classical signals, Phys. Rev. Lett.119, 050801 (2017)

work page 2017

[27] [27]

Tsang, H

M. Tsang, H. M. Wiseman, and C. M. Caves, Fundamental quantum limit to waveform estimation, Phys. Rev. Lett.106, 090401 (2011)

work page 2011

[28] [28]

F.Ya.Khalili, Sensitivity limit for continous measurement of the quantum probe position, Doklady Akademii Nauk294, 602 (1987), (in Russian; see also [8], Chapter VIII)

work page 1987

[29] [29]

F. Y. Khalili and E. Zeuthen, Quantum limits for stationary force sensing, Phys. Rev. A103, 043721 (2021)

work page 2021

[30] [30]

Braginsky and F

V. Braginsky and F. Khalili, Low noise rigidity in quantum measurements, Physics Letters A257, 241 (1999)

work page 1999

[31] [31]

A.Buonanno, Y.Chen, Signal recycled laser-interferometer gravitational-wave detectors as optical springs, Physical Review D65, 042001 (2002). 10

work page 2002

[32] [32]

R.Kubo, A general expression for the conductivity tensor, Canadian Journal of Physics34, 1274 (1956)

work page 1956

[33] [33]

I.Vorontsov and F

Yu. I.Vorontsov and F. Ya. Khalili, Quantum-mechanical limitations in classical analysis of schemes with amplifiers, Radio Engineering and Electronic Physics27, 2392 (1982), (in Russian; see also [8], Chapter VI)

work page 1982