Pith. sign in

REVIEW 2 major objections 5 minor 116 references

Quantum metrology through spectral measurements in quantum optics

T0 review · 2 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Frequency-resolved photon counting can be made optimal for sensing emitter parameters by combining spectral filters with a coherent displacement of the detected field.

desk verdict A genuinely new framework for frequency-resolved metrology, with a fixable but load-bearing inconsistency in the two-sensor appendix that must be resolved before the headline gain can be trusted. read the letter →

arxiv 2509.04300 v2 pith:5HQBJ2BY submitted 2025-09-04 quant-ph cond-mat.mes-hallphysics.optics

Alejandro Vivas-Viaña , Carlos Sánchez Muñoz This is my paper · ORCID
classification quant-phcond-mat.mes-hallphysics.optics MSC 81V8081P50 PACS 42.50.-p03.65.Ta
keywords quantummetrologyfrequency-resolvedphotoncountingFisherinformationresonancefluorescencecascadedsystemsmean-fieldengineeringMollowtripletsensing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper sets out to quantify how much metrological information can be extracted from the frequency-resolved light emitted by a continuously driven quantum system. Modeling spectral filters as cascaded bosonic sensors, the authors compute the full photon-counting statistics of the filtered modes and the associated classical Fisher information, and show that both filter frequency and linewidth strongly control estimation precision, with an optimal linewidth window roughly between 10^-2 times and 10 times the Rabi frequency. They find that coherently displacing the detected field before photon counting—mean-field engineering—can push the classical Fisher information up to the quantum Fisher information of the sensor modes, effectively realizing the optimal measurement. In a two-sensor setup, retaining photon-photon cross-correlations yields a metrological gain that can reach five orders of magnitude near Mollow leapfrog transitions when estimating the qubit-laser detuning, and the paper proves a general bound showing joint detection always gives at least half the sum of the marginal Fisher informations. The relevance is that spectral filtering, already ubiquitous in experiments, can be turned into a principled quantum sensing tool.

What carries the argument

The central object is the cascaded-sensor master equation: each frequency filter is a bosonic mode with detuning Delta_xi and linewidth Gamma, driven by the emitter's output field through a cascaded coupling, so that the filtered radiation is described by a finite-dimensional density matrix. The workhorse quantities are the diagonal elements of that density matrix—the photon-counting probabilities—whose parameter derivatives define the classical Fisher information, and the coherent displacement operator D(alpha) that implements mean-field engineering by mixing the signal with a local oscillator before counting. This machinery converts a measurement-theoretic question (what can be learned fro

What would settle it

Recompute the two-sensor classical Fisher information at the leapfrog point (Delta1, Delta2) approximately (-2 Omega + delta_omega, 2 Omega) using the cross-coupling coefficient sqrt(epsilon gamma Gamma) instead of sqrt(epsilon gamma Gamma / 2), and check whether F_Delta / F_Delta^I remains near 10^5. An experimental alternative: measure the joint photon-counting distribution of resonance fluorescence at those two frequencies with a tunable filter linewidth and compare the empirical Fisher information with the two predictions.

Watch

Extended reading notes

Core claim

The central claim is that frequency-resolved photon counting on light emitted by a coherently driven two-level emitter can be made optimal for parameter estimation, provided the filtered modes are modeled correctly and the measurement is chosen well. The authors model each filter as a bosonic sensor in a cascaded master equation, reconstruct its steady-state density matrix and its derivative, and use these to evaluate the classical Fisher information of the photon-number distribution. They show that the single-sensor classical Fisher information displays a Mollow-triplet-like spectrum with additional features tied to higher-order photon correlations, that a sensor linewidth in the window Gam

Load-bearing premise

The load-bearing premise is that the cascaded coupling coefficient in the two-sensor master equation is sqrt(epsilon gamma Gamma / 2), as written in Eq. (4); the appendix derivation instead gives sqrt(epsilon gamma Gamma), and if the appendix is right, every two-sensor Fisher information value, including the reported 10^5 gain, changes.

Editorial extensions

If this is right

  • For any driven emitter described by a Lindblad master equation, the same construction yields the optimal filter frequency and linewidth for estimating a given parameter, making spectral filtering a systematic metrological resource rather than an ad hoc tool.
  • Near the optimal linewidth window, the single-sensor classical Fisher information is enhanced by over ten orders of magnitude relative to the narrowband and broadband limits, so filter bandwidth is a first-order control knob for sensitivity.
  • An experimentalist who can add a tunable local oscillator to a spectral filter can, in principle, reach the quantum Fisher information of the filtered mode without designing a more complex POVM.
  • Joint detection on two frequency channels can beat independent measurements by up to five orders of magnitude when the parameter is the detuning and the channels sit on a Mollow leapfrog transition; this makes Hanbury-Brown-Twiss-style setups useful for metrology, not just for correlation measurements.
  • The inequality F_theta[joint] >= 1/2(F_theta[marginal1] + F_theta[marginal2]) holds generally, so joint measurements can never lose more than a factor of two, but also guarantees no universal advantage of correlations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same framework should apply to other continuously driven sources with richer spectra, where the optimal filtering strategies will likely differ; the paper's qualitative conclusion—correlations help for some parameters and not others—implies that parameter-specific optimization is essential.
  • The factor sqrt(2) discrepancy between the two-sensor master equation in Eq. (4) and its derivation in Appendix A.2 is a load-bearing detail: if the appendix is correct, all quantitative two-sensor results, including the claimed 10^5 gain and the optimal linewidth windows, need to be recomputed, although the qualitative mechanism may survive.
  • One could test the general bound experimentally by measuring the joint and marginal photon-counting distributions of a resonance-fluorescence source and comparing their Fisher informations; the bound predicts the joint information is never less than half the sum of the marginals.
  • Mean-field engineering could be combined with spectral filtering in a single setup, potentially allowing parameter estimation at the sensor quantum Fisher information while retaining frequency selectivity.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper develops a cascaded-sensor theoretical framework to quantify the metrological information contained in frequency-filtered photon-counting measurements from a continuously driven two-level emitter. It defines frequency-resolved classical Fisher information (CFI), compares it with the quantum Fisher information (QFI) of the filtered sensor modes, and introduces coherent displacement ('mean-field engineering') as a tunable measurement strategy. In the single-sensor setting, it identifies frequency windows and optimal sensor linewidths, and reports that an optimally chosen displacement can saturate the sensor QFI. It then extends the framework to two sensors coupled to the source through a balanced beam splitter, showing that joint photon counting can exceed independent-detection Fisher information by up to five orders of magnitude near leapfrog resonances. It also proves a general bound, Eq. (19), relating the joint and marginal Fisher informations.

Significance. If the central claims survive scrutiny, the paper makes a useful contribution: it provides a concrete, physically motivated method for benchmarking frequency-resolved measurements in quantum optics, and it identifies a specific measurement strategy—displaced photon counting—that can numerically saturate the QFI of the filtered modes. The proof of Eq. (19) is valuable and independent of the disputed coupling coefficient. The predicted large metrological enhancement from two-photon leapfrog correlations is interesting and falsifiable. The main caveat is that the two-sensor quantitative results rest on a master-equation coupling coefficient that is internally inconsistent; the single-sensor results and the bound in Eq. (19) are not affected.

major comments (2)
  1. The two-sensor master equation contains an internal inconsistency. Eq. (4) has cross-coupling coefficient sqrt(ε γ Γ_i / 2), whereas the derivation in Appendix A.2, Eq. (A12), after the stated identifications Γ1→γ, Γ2→Γ, and sqrt(Γ1Γ2)→sqrt(εγΓ), yields coefficient sqrt(εγΓ) — a factor √2 larger. The sentence after Eq. (4) says the 1/√2 accounts for vacuum contributions from the balanced beam splitter, but the beam-splitter input relation (A8) and collective operator (A10) do not introduce a final 1/√2 in the dissipative cross term (A12). Since Eq. (4) determines all two-sensor CFI values, the g^(2) maps, and the headline F_Δ ≈ 10^5 F_Δ^I in Figs. 5 and 6, the two versions cannot both be correct. Please correct one of them. If the corrected coupling differs from Eq. (4), recompute all two-sensor results and state whether the order-of-magnitude gain survives and how the optimal linewidth
  2. The numerical CFI and QFI require truncating the bosonic sensor Hilbert spaces, but the manuscript does not report the truncation level n_exc or a convergence test. This matters especially for the saturation claim in §III.C: optimal displacements with |α| ~ 4 (Fig. 4) populate many Fock states, so F_α,θ and I_θ must be checked as functions of truncation. Please state the truncation used and demonstrate convergence for the quantities plotted in Figs. 4–6. This is also needed to assess the magnitude of the claimed deviations from QFI saturation near resonance.
minor comments (5)
  1. The main text says 'the bound presented in Eq. (18)' but Eq. (18) defines F^I_θ; the actual bound is Eq. (19). Appendix I also says 'Eq. (18)' in its opening sentence. Please correct the cross-reference.
  2. Typo: 'For the shake of simplicity' should be 'For the sake of simplicity'.
  3. The range 'Γ ∈ (10^-2, 10)Ω' is ambiguous; it should be written as Γ ∈ (10^{-2}Ω, 10Ω) or similar.
  4. The parameter value 'Ω = γ/2√γ' appears dimensionally inconsistent; it should be made consistent with the text (e.g., Ω = γ/(2√2) or a stated value in units of γ).
  5. There is a duplicated and slightly garbled sentence: 'This behaviour is similar to what occurs for θ=γ, except...' appears twice with different wording. Please revise.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Fisher information values are computed from an explicit cascaded master equation and independent QFI bounds; the only noteworthy issue is an internal √2 consistency concern in the two-sensor model, which is a correctness risk rather than a circular reduction.

full rationale

I find no load-bearing circularity. The core quantities—single- and two-sensor CFI, SNR, and sensor QFI—are computed by solving the cascaded master equations (Eqs. (3) and (4)) for the steady state and its parameter derivative (Appendix B), not by fitting the target estimation results. The optimal displacement α_opt is obtained by explicitly maximizing F^α_θ over displacements; the subsequent claim that F^α_opt saturates I_θ is a nontrivial comparison against the independently computed quantum Fisher information over all POVMs, not a tautology. Similarly, the displacement α_fluct that isolates quantum fluctuations is derived from a mean-field linearization in Appendix F, not assumed. The two-sensor advantage F_θ / F^I_θ is evaluated from the joint distribution constructed in Eq. (16), while the uncorrelated benchmark F^I_θ is defined as the sum of marginals in Eq. (18); the comparison is therefore meaningful. The general bound in Eq. (19) is proven via Sedrakyan's/Cauchy-Schwarz inequality in Appendix I and does not depend on the numerical model. Self-citations to Refs. [40], [44], and [89] are used as background or to distinguish prior setups; the load-bearing material (master equation, PFI, correlator inversion) is derived in the appendices, so these citations are not load-bearing. The manuscript even includes an honest caveat that the sensor QFI bounds only the filtered modes, not the full radiated field. The factor-√2 discrepancy between Eq. (4) and Eq. (A12) is a genuine internal-consistency concern that could change the two-sensor numerics, but it is not a case of a prediction reducing to its inputs by construction; it is a consistency/correctness issue, so it does not raise the circularity score.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

No data fitting is performed and no new physical entities are introduced. The model parameters Omega, gamma, Delta, Gamma, epsilon are scanned, and alpha_opt is an optimized measurement knob. The main hidden ingredient is the unspecified Fock-space truncation order used in the numerical solutions.

free parameters (3)
  • coherent displacement alpha_opt = frequency-dependent complex number, e.g., alpha_opt ~ 3.95 - 1.56i in Fig. 4(a)
    Chosen numerically to maximize the CFI at each frequency; not fitted to data, but selected to reach the QFI, so it is a control knob rather than a hidden parameter.
  • sensor linewidth Gamma = scanned values such as 10^-1 gamma, 1 gamma, 10 gamma; optimal window stated as (10^-2 Omega, 10 Omega)
    The central tuning parameter of the study; scanned by hand over ranges, not estimated from data.
  • coupling efficiency epsilon = epsilon = 0.1, 0.5, 1 in various figures
    Model parameter accounting for losses; chosen by hand to explore imperfect coupling.
assumptions (6)
  • domain assumption Rotating wave approximation and Markovian Lindblad master equation for the driven two-level emitter
    Eqs. (1)-(2); standard in quantum optics, assumed valid for the regimes considered.
  • domain assumption Cascaded quantum systems formalism: source output feeds the sensors one-way without back-action
    Eqs. (3)-(4) and Appendix A; based on Gardiner-Carmichael cascaded theory, a standard but domain-specific model.
  • domain assumption Frequency filters are modeled as single-mode bosonic cavities with Lorentzian linewidth
    Sensors with detuning Delta_xi and linewidth Gamma; follows Refs. 41-44; physically motivated but a modeling choice.
  • domain assumption Photon-counting probabilities are expressed as finite sums over normally ordered correlators (Eq. 11) with an implicit truncation
    Adopted from Refs. 60 and 86; the truncation order nexc is not specified in the main text, which is a hidden numerical assumption.
  • standard math Sedrakyan's inequality (reformulation of Cauchy-Schwarz) used to derive the joint vs independent CFI bound
    Appendix I; standard algebraic inequality, uncontroversial.
  • standard math Existence and uniqueness of the steady state of the Liouvillian, and validity of trace-normalization replacement
    Appendix B; relies on Evans' theorem and standard open quantum systems results.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum metrology through spectral measurements in quantum optics." pith.science (2026). https://pith.science/paper/5HQBJ2BY

@misc{pith2026250904300,
  author       = {Pith},
  title        = {Pith review of: Quantum metrology through spectral measurements in quantum optics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5HQBJ2BY}},
  note         = {Machine review of arXiv:2509.04300}
}
read the original abstract

Continuously monitored quantum systems are emerging as promising platforms for quantum metrology, where a central challenge is to identify measurement strategies that optimally extract information about unknown parameters encoded in the complex quantum state of emitted radiation. Different measurement strategies effectively access distinct temporal modes of the emitted field, and the resulting choice of mode can strongly impact the information available for parameter estimation. While a ubiquitous approach in quantum optics is to select frequency modes through spectral filtering, the metrological potential of this technique has not yet been systematically quantified. We develop a theoretical framework to assess this potential by modeling spectral detection as a cascaded quantum system, allowing us to reconstruct the full density matrix of frequency-filtered photonic modes and to compute their associated Fisher information. This framework provides a minimal yet general method to benchmark the performance of spectral measurements in quantum optics, allowing to identify optimal filtering strategies in terms of frequency selection, detector linewidth, and metrological gain accessible through higher-order frequency-resolved correlations and mean-field engineering. These results lay the groundwork for identifying and designing optimal sensing strategies in practical quantum-optical platforms.

Figures

Figures reproduced from arXiv: 2509.04300 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Sketch of the metrological setup. A coherently driven emitter, characterized by atomic parameters to be [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Frequency-resolved Fisher information for one [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Impact of sensor linewidth Γ on the performance [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Optimizing quantum parameter estimation via [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Frequency-resolved Fisher information for two sensor to estimate [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Impact of sensor linewidth Γ on the performance of [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Schematic representation of cascaded systems. (a) A [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Frequency-resolved Fisher information for one [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Impact of imperfect system-sensor coupling ( [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Frequency-resolved Fisher information for two [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

116 extracted references · 74 canonical work pages

  1. [1]

    This enables the description of setups driven by general sources of light

    Single-sensor cascaded master equation In a cascaded quantum system, the output field of a system (the source) is fed into the input of another sys- tem (the target), without any back-action from the tar- get to the source. This enables the description of setups driven by general sources of light. This is formally de- scribed by the cascaded formalism [60...

  2. [2]

    Two-sensor cascaded master equation As discussed in the main text, extending the cascaded formalism to multiple target systems requires careful con- sideration, as different configurations lead to both quan- titatively and qualitatively different dynamics. In this work, we focus on a specific configuration in which the emission from the source (system 1) ...

  3. [3]

    Computation of the steady-state Let us assume an arbitrary open quantum system whose dynamics is described by a Lindblad master equa- tion: dˆρ dt = −i[ ˆH, ˆρ] + X i D[ ˆLi]ˆρ, (B1) where ˆH is the Hamiltonian, D[ ˆLi] is a general Lindblad term defined via the jump operator ˆLi, and ˆρ is the re- duced density matrix describing the quantum system. By ca...

  4. [4]

    This is achieved by taking the derivative with respect θ in (B2), such that ∂θ[ ˆLˆρss] = (∂θ ˆL)ˆρss + ˆL∂θ ˆρss = 0, (B6) and get the relation ∂θ ˆρss = − ˆL−1(∂θ ˆL)ˆρss

    Computation of the differentiation of the steady-state The formal relation from (B5) can be extended to com- pute the differentation of the steady-state density matrix with respect to a system parameter θ, denoted as ∂θ ˆρss. This is achieved by taking the derivative with respect θ in (B2), such that ∂θ[ ˆLˆρss] = (∂θ ˆL)ˆρss + ˆL∂θ ˆρss = 0, (B6) and get...

  5. [5]

    [89, 90], we assume that the resulting state of the sensor is a coherent state, so that the corresponding measured photo-current displays Poissonian fluctuations

    Derivation Following the same approach that is used in Refs. [89, 90], we assume that the resulting state of the sensor is a coherent state, so that the corresponding measured photo-current displays Poissonian fluctuations. Under 16 this assumption, for a sensor at frequencyωξ, the photon- counting distribution is given by: p(n|θ) = ¯nne−¯n n! , (E1) wher...

  6. [6]

    In particular, the classical Fisher information (CFI) may not always outperform the Fisher information obtained under a Poissonian approximation

    Poissonian Fisher information bound Although it is intuitive to assume that a full statistical description of light yields higher sensitivity in metrolog- ical protocols, this is not mathematically guaranteed. In particular, the classical Fisher information (CFI) may not always outperform the Fisher information obtained under a Poissonian approximation. T...

  7. [7]

    4(a)], the mean-field engineering technique is implemented by means of an unbalanced beam splitter combined with a local oscillator in the limit of perfect transmittance

    General method As explained in the main text [see inset Fig. 4(a)], the mean-field engineering technique is implemented by means of an unbalanced beam splitter combined with a local oscillator in the limit of perfect transmittance. In this scenario, the sensor receives the output field dis- placed by a complex amplitude α in phase space. Formally, this pr...

  8. [8]

    Here, we determine the specific value of the displacement parameter α that can- cels the coherent component of the signal, isolating only the quantum fluctuations

    Isolating quantum fluctuations In the previous section, we described how to coher- ently displace a sensor state via a classical field to im- plement mean-field engineering. Here, we determine the specific value of the displacement parameter α that can- cels the coherent component of the signal, isolating only the quantum fluctuations. For practical purpo...

Show all 116 references
  1. [9]

    Proof We consider two bosonic modes with Hilbert spaces, H1 and H2, both truncated up to N + 1 excitations, such that the Hilbert space is H = H1 ⊗H 2. A general density matrix ˆρ in this space can be expanded in the Fock basis as: ˆρ = NX n1,n2=0 Pn1,n2 |n1n2⟩⟨n1n2| + off-dia...

  2. [10]

    The total probability must sum one, NX n1,n2=0 Pn1,n2 = 1 (H6)

    Normalization. The total probability must sum one, NX n1,n2=0 Pn1,n2 = 1 (H6)

  3. [11]

    Marginal distributions. The reduced single-mode distributions must agree with the marginals of Pn1,n2 , Pn1 = NX n2=0 Pn1,n2 , (H7a) Pn2 = NX n1=0 Pn1,n2 , (H7b) such that P0,0 = 1 − X n1,n2̸=0 Pn1,n2 (H8a) Pn1,0 = Pn1 − NX n1̸=0,n2̸=0 Pn1,n2 , (H8b) P0,n2 = Pn2 − NX n1̸=0,n2̸...

  4. [12]

    Extension to N bosonic modes This procedure can be generalized to any number of modes. For an N -mode system [H = NN i=1 Hi], the joint distribution Pn1,n2,...,nN can be reconstructed via a multi- dimensional extension of the same formula: Pn1,n2,...,nN = nexcX j1≥n1 nexcX j2≥...

  5. [13]

    Mabuchi and P

    H. Mabuchi and P. Zoller, Inversion of Quantum Jumps in Quantum Optical Systems under Continuous Obser- vation, Physical Review Letters 76, 3108 (1996)

    1996

  6. [14]

    Gambetta and H

    J. Gambetta and H. M. Wiseman, State and dynam- ical parameter estimation for open quantum systems, Physical Review A 64, 042105 (2001)

    2001

  7. [15]

    Tsang, Continuous Quantum Hypothesis Testing, Physical Review Letters 108, 170502 (2012)

    M. Tsang, Continuous Quantum Hypothesis Testing, Physical Review Letters 108, 170502 (2012)

    2012

  8. [16]

    D. Yang, S. F. Huelga, and M. B. Plenio, Efficient Infor- mation Retrieval for Sensing via Continuous Measure- ment, Physical Review X 13, 031012 (2023)

    2023

  9. [17]

    H. M. Wiseman and G. J. Milburn, Quantum Measure- ment and Control(Cambridge University Press, 2014)

    2014

  10. [18]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Reviews of Modern Physics 89, 035002 (2017)

    2017

  11. [19]

    Braun, G

    D. Braun, G. Adesso, F. Benatti, R. Floreanini, U. Mar- zolino, M. W. Mitchell, and S. Pirandola, Quantum- enhanced measurements without entanglement, Re- views of Modern Physics 90, 035006 (2018)

    2018

  12. [20]

    Gammelmark and K

    S. Gammelmark and K. Mølmer, Bayesian parameter in- ference from continuously monitored quantum systems, Physical Review A 87, 032115 (2013)

    2013

  13. [21]

    Cortez, A

    L. Cortez, A. Chantasri, L. P. Garc ´ ıa-Pintos, J. Dres- sel, and A. N. Jordan, Rapid estimation of drifting pa- rameters in continuously measured quantum systems, Physical Review A 95, 012314 (2017)

    2017

  14. [22]

    Albarelli, M

    F. Albarelli, M. A. C. Rossi, M. G. A. Paris, and M. G. Genoni, Ultimate limits for quantum magnetometry via time-continuous measurements, New Journal of Physics 19, 123011 (2017)

    2017

  15. [23]

    J. A. Gross, C. M. Caves, G. J. Milburn, and J. Combes, Qubit models of weak continuous measure- ments: Markovian conditional and open-system dynam- ics, Quantum Science and Technology 3, 024005 (2018)

    2018

  16. [24]

    Shankar, G

    A. Shankar, G. P. Greve, B. Wu, J. K. Thompson, and M. Holland, Continuous Real-Time Tracking of a Quan- tum Phase Below the Standard Quantum Limit, Phys- ical Review Letters 122, 233602 (2019)

    2019

  17. [25]

    Fallani, M

    A. Fallani, M. A. C. Rossi, D. Tamascelli, and M. G. Genoni, Learning Feedback Control Strategies for Quantum Metrology, PRX Quantum 3, 020310 (2022)

    2022

  18. [26]

    Khanahmadi and K

    M. Khanahmadi and K. Mølmer, Qubit readout and quantum sensing with pulses of quantum radiation, Physical Review A 107, 013705 (2023)

    2023

  19. [27]

    Ilias, D

    T. Ilias, D. Yang, S. F. Huelga, and M. B. Plenio, Criticality-enhanced electric field gradient sensor with single trapped ions, npj Quantum Information 10, 36 (2024)

    2024

  20. [28]

    Cabot, F

    A. Cabot, F. Carollo, and I. Lesanovsky, Quantum en- hanced parameter estimation with monitored quantum nonequilibrium systems using inefficient photo detection (2025), arXiv:2503.21753 [quant-ph]

    2025

  21. [29]

    G´ orecki, F

    W. G´ orecki, F. Albarelli, S. Felicetti, R. Di Candia, and L. Maccone, Interplay Between Time and Energy in Bosonic Noisy Quantum Metrology, PRX Quantum 6, 020351 (2025)

    2025

  22. [30]

    G´ orecki, S

    W. G´ orecki, S. Felicetti, L. Maccone, and R. D. Candia, Time correlations from steady-state expectation values 22 (2025), arXiv:2507.08661 [quant-ph]

    2025 arXiv

  23. [31]

    Amor´ os-Binefa and J

    J. Amor´ os-Binefa and J. Ko lody´ nski, Noisy atomic mag- netometry in real time, New Journal of Physics 23, 123030 (2021)

    2021

  24. [32]

    Amor´ os-Binefa and J

    J. Amor´ os-Binefa and J. Ko lody´ nski, Noisy Atomic Magnetometry with Kalman Filtering and Measurement-Based Feedback, PRX Quantum 6, 030331 (2025)

    2025

  25. [33]

    Barzanjeh, A

    S. Barzanjeh, A. Xuereb, S. Gr¨ oblacher, M. Paternos- tro, C. A. Regal, and E. M. Weig, Optomechanics for quantum technologies, Nature Physics 18, 15 (2022)

    2022

  26. [34]

    S. L. Danilishin and F. Y. Khalili, Quantum Measure- ment Theory in Gravitational-Wave Detectors, Living Reviews in Relativity 15, 5 (2012)

    2012

  27. [35]

    Ilias, D

    T. Ilias, D. Yang, S. F. Huelga, and M. B. Plenio, Criticality-Enhanced Quantum Sensing via Continuous Measurement, PRX Quantum 3, 010354 (2022)

    2022

  28. [36]

    Macieszczak, M

    K. Macieszczak, M. Gut ¸˘ a, I. Lesanovsky, and J. P. Gar- rahan, Dynamical phase transitions as a resource for quantum enhanced metrology, Physical Review A 93, 022103 (2016)

    2016

  29. [37]

    Fern´ andez-Lorenzo and D

    S. Fern´ andez-Lorenzo and D. Porras, Quantum sensing close to a dissipative phase transition: Symmetry break- ing and criticality as metrological resources, Physical Review A 96, 013817 (2017)

    2017

  30. [38]

    Di Candia, F

    R. Di Candia, F. Minganti, K. V. Petrovnin, G. S. Paraoanu, and S. Felicetti, Critical parametric quantum sensing, npj Quantum Information 9, 23 (2023)

    2023

  31. [39]

    V. P. Pavlov, D. Porras, and P. A. Ivanov, Quantum metrology with critical driven-dissipative collective spin system, Physica Scripta 98, 095103 (2023)

    2023

  32. [40]

    Montenegro, M

    V. Montenegro, M. G. Genoni, A. Bayat, and M. G. A. Paris, Quantum metrology with boundary time crystals, Communications Physics 6, 304 (2023)

    2023

  33. [41]

    Cabot, F

    A. Cabot, F. Carollo, and I. Lesanovsky, Exploiting nonequilibrium phase transitions and strong symmetries for continuous measurement of collective observables, Physical Review A 110, L060601 (2024)

    2024

  34. [42]

    Cabot, F

    A. Cabot, F. Carollo, and I. Lesanovsky, Continuous Sensing and Parameter Estimation with the Bound- ary Time Crystal, Physical Review Letters 132, 050801 (2024)

    2024

  35. [43]

    Alushi, A

    U. Alushi, A. Coppo, V. Brosco, R. Di Candia, and S. Felicetti, Collective quantum enhancement in critical quantum sensing, Communications Physics8, 74 (2025)

    2025

  36. [44]

    Mattes, A

    R. Mattes, A. Cabot, F. Carollo, and I. Lesanovsky, De- signing open quantum systems for enabling quantum en- hanced sensing through classical measurements (2025), arXiv:2505.08756 [quant-ph]

    2025

  37. [45]

    Ding, Z.-K

    D.-S. Ding, Z.-K. Liu, B.-S. Shi, G.-C. Guo, K. Mølmer, and C. S. Adams, Enhanced metrology at the critical point of a many-body Rydberg atomic system, Nature Physics 18, 1447 (2022)

    2022

  38. [46]

    Gammelmark and K

    S. Gammelmark and K. Mølmer, Fisher Information and the Quantum Cram´ er-Rao Sensitivity Limit of Con- tinuous Measurements, Physical Review Letters 112, 170401 (2014)

    2014

  39. [47]

    Catana, L

    C. Catana, L. Bouten, and M. Gut ¸˘ a, Fisher informa- tions and local asymptotic normality for continuous- time quantum Markov processes, Journal of Physics A: Mathematical and Theoretical 48, 365301 (2015)

    2015

  40. [48]

    A. H. Kiilerich and K. Mølmer, Parameter estimation by multichannel photon counting, Physical Review A 91, 012119 (2015)

    2015

  41. [49]

    Godley and M

    A. Godley and M. Guta, Adaptive measurement filter: Efficient strategy for optimal estimation of quantum Markov chains, Quantum 7, 973 (2023)

    2023

  42. [50]

    A. H. Kiilerich and K. Mølmer, Input-Output Theory with Quantum Pulses, Physical Review Letters 123, 123604 (2019)

    2019

  43. [51]

    A. H. Kiilerich and K. Mølmer, Quantum interactions with pulses of radiation, Physical Review A102, 023717 (2020)

    2020

  44. [52]

    J. Yang, I. Strandberg, A. Vivas-Via˜ na, A. Gaikwad, C. Castillo-Moreno, A. F. Kockum, M. A. Ullah, C. S. Mu˜ noz, A. M. Eriksson, and S. Gasparinetti, Entangle- ment of photonic modes from a continuously driven two- level system, npj Quantum Information 11, 69 (2025)

    2025

  45. [53]

    J. H. Eberly and K. W´ odkiewicz, The time-dependent physical spectrum of light, Journal of the Optical Soci- ety of America 67, 1252 (1977)

    1977

  46. [54]

    Del Valle, A

    E. Del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Teje- dor, and M. J. Hartmann, Theory of Frequency-Filtered and Time-Resolved N -Photon Correlations, Physical Review Letters 109, 183601 (2012)

    2012

  47. [55]

    J. C. L. Carre˜ no and F. P. Laussy, Excitation with quan- tum light. I. Exciting a harmonic oscillator, Physical Review A 94, 063825 (2016)

    2016

  48. [56]

    J. C. L. Carre˜ no, C. S´ anchez Mu˜ noz, E. Del Valle, and F. P. Laussy, Excitation with quantum light. II. Excit- ing a two-level system, Physical Review A 94, 063826 (2016)

    2016

  49. [57]

    Peiris, B

    M. Peiris, B. Petrak, K. Konthasinghe, Y. Yu, Z. C. Niu, and A. Muller, Two-color photon correlations of the light scattered by a quantum dot, Physical Review B 91, 195125 (2015)

    2015

  50. [58]

    Peiris, K

    M. Peiris, K. Konthasinghe, and A. Muller, Franson In- terference Generated by a Two-Level System, Physical Review Letters 118, 030501 (2017)

    2017

  51. [59]

    Ulhaq, S

    A. Ulhaq, S. Weiler, S. M. Ulrich, R. Roßbach, M. Jet- ter, and P. Michler, Cascaded single-photon emission from the Mollow triplet sidebands of a quantum dot, Nature Photonics 6, 238 (2012)

    2012

  52. [60]

    Silva, C

    B. Silva, C. S´ anchez Mu˜ noz, D. Ballarini, A. Gonz´ alez- Tudela, M. De Giorgi, G. Gigli, K. West, L. Pfeiffer, E. Del Valle, D. Sanvitto, and F. P. Laussy, The col- ored Hanbury Brown–Twiss effect, Scientific Reports 6, 37980 (2016)

    2016

  53. [61]

    Gonzalez-Tudela, F

    A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, M. J. Hartmann, and E. del Valle, Two-photon spectra of quantum emitters, New Journal of Physics 15, 033036 (2013)

    2013

  54. [62]

    S´ anchez Mu˜ noz, E

    C. S´ anchez Mu˜ noz, E. Del Valle, C. Tejedor, and F. P. Laussy, Violation of classical inequalities by photon fre- quency filtering, Physical Review A 90, 052111 (2014)

    2014

  55. [63]

    J. C. L´ opez Carre˜ no, E. Del Valle, and F. P. Laussy, Photon Correlations from the Mollow Triplet, Laser & Photonics Reviews 11, 1700090 (2017)

    2017

  56. [64]

    Zubizarreta Casalengua, J

    E. Zubizarreta Casalengua, J. C. L´ opez Carre˜ no, F. P. Laussy, and E. del Valle, Conventional and Unconven- tional Photon Statistics, Laser & Photonics Reviews14, 1900279 (2020)

    2020

  57. [65]

    J. C. L´ opez Carre˜ no, S. Berm´ udez Feijoo, and M. Stobi´ nska, Entanglement in Resonance Fluorescence, npj Nanophotonics 1, 3 (2024)

    2024

  58. [66]

    M. K. Schmidt, R. Esteban, G. Giedke, J. Aizpurua, and A. Gonz´ alez-Tudela, Frequency-resolved photon corre- lations in cavity optomechanics, Quantum Science and 23 Technology 6, 034005 (2021)

    2021

  59. [67]

    M. ´A. Mart ´ ınez-Garc ´ ıa and D. Mart ´ ın-Cano, Coherent Electron-Vibron Interactions in Surface-Enhanced Ra- man Scattering (SERS), Physical Review Letters 132, 093601 (2024)

    2024

  60. [68]

    Moradi Kalarde, F

    F. Moradi Kalarde, F. Ciccarello, C. S´ anchez Mu˜ noz, J. Feist, and C. Galland, Photon antibunching in single-molecule vibrational sum-frequency generation, Nanophotonics 14, 59 (2025)

    2025

  61. [69]

    H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2007)

    2007

  62. [70]

    Carmichael, An Open Systems Approach to Quantum Optics, Lecture Notes in Physics Monographs, Vol

    H. Carmichael, An Open Systems Approach to Quantum Optics, Lecture Notes in Physics Monographs, Vol. 18 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1993)

    1993

  63. [71]

    J. J. Garc ´ ıa Ripoll,Quantum Information and Quantum Optics with Superconducting Circuits, 1st ed. (Cam- bridge University Press, 2022)

    2022

  64. [72]

    C. W. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Op- tics, 3rd ed., Springer Series in Synergetics (Springer, Berlin ; New York, 2004)

    2004

  65. [73]

    J. C. L´ opez Carre˜ no, E. Del Valle, and F. P. Laussy, Frequency-resolved Monte Carlo, Scientific Reports 8, 6975 (2018)

    2018

  66. [74]

    J. P. Dowling and K. P. Seshadreesan, Quantum Opti- cal Technologies for Metrology, Sensing, and Imaging, Journal of Lightwave Technology 33, 2359 (2015)

    2015

  67. [75]

    J. Liu, H. Yuan, X.-M. Lu, and X. Wang, Quantum Fisher information matrix and multiparameter estima- tion, Journal of Physics A: Mathematical and Theoret- ical 53, 023001 (2020)

    2020

  68. [76]

    M. G. A. Paris, QUANTUM ESTIMATION FOR QUANTUM TECHNOLOGY, International Journal of Quantum Information 07, 125 (2009)

    2009

  69. [77]

    Petz and D

    D. Petz and D. Ghinea, Introduction to quantum fisher information, in Quantum Probability and Related Topics (World Scientific, 2011) pp. 261–281

    2011

  70. [78]

    H. M. Wiseman and G. J. Milburn, Quantum Measure- ment and Control, 1st ed. (Cambridge University Press, 2009)

    2009

  71. [79]

    Demkowicz-Dobrza´ nski, M

    R. Demkowicz-Dobrza´ nski, M. Jarzyna, and J. Ko lody´ nski, Quantum Limits in Optical Inter- ferometry, in Progress in Optics , Vol. 60 (Elsevier,

  72. [80]

    Pezz` e, A

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

    2018

  73. [81]

    Polino, M

    E. Polino, M. Valeri, N. Spagnolo, and F. Sciarrino, Photonic quantum metrology, A VS Quantum Science2, 024703 (2020)

    2020

  74. [82]

    Barbieri, Optical Quantum Metrology, PRX Quan- tum 3, 010202 (2022)

    M. Barbieri, Optical Quantum Metrology, PRX Quan- tum 3, 010202 (2022)

    2022

  75. [83]

    Zubizarreta Casalengua, J

    E. Zubizarreta Casalengua, J. C. L´ opez Carre˜ no, F. P. Laussy, and E. del Valle, Tuning photon statistics with coherent fields, Physical Review A 101, 063824 (2020)

    2020

  76. [84]

    S. K. Kim, E. Z. Casalengua, K. Boos, F. Sbresny, C. Calcagno, H. Riedl, J. J. Finley, C. Ant´ on-Solanas, F. P. Laussy, K. M¨ uller, L. Hanschke, and E. del Valle, Unlocking multiphoton emission from a single- photon source through mean-field engineering (2024), arXiv:2411.10...

    2024 arXiv

  77. [85]

    T´ oth and I

    G. T´ oth and I. Apellaniz, Quantum metrology from a quantum information science perspective, Journal of Physics A: Mathematical and Theoretical 47, 424006 (2014)

    2014

  78. [86]

    M. M. Rams, P. Sierant, O. Dutta, P. Horodecki, and J. Zakrzewski, At the Limits of Criticality-Based Quan- tum Metrology: Apparent Super-Heisenberg Scaling Revisited, Physical Review X 8, 021022 (2018)

    2018

  79. [87]

    Cram´ er,Mathematical Methods of Statistics, Prince- ton Mathematical Series No

    H. Cram´ er,Mathematical Methods of Statistics, Prince- ton Mathematical Series No. 9 (Princeton university press, Princeton, 1991)

    1991

  80. [88]

    C. R. Rao, Information and the Accuracy Attainable in the Estimation of Statistical Parameters, in Break- throughs in Statistics, edited by S. Kotz and N. L. John- son (Springer New York, New York, NY, 1992) pp. 235– 247

    1992

  81. [89]

    Lodahl, S

    P. Lodahl, S. Mahmoodian, and S. Stobbe, Interfac- ing single photons and single quantum dots with pho- tonic nanostructures, Reviews of Modern Physics 87, 347 (2015)

    2015

  82. [90]

    E. B. Flagg, A. Muller, J. W. Robertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, G. J. Salamo, and C. K. Shih, Resonantly driven coherent oscillations in a solid- state quantum emitter, Nature Physics 5, 203 (2009)

    2009

  83. [91]

    H. J. Kimble and L. Mandel, Theory of resonance fluo- rescence, Physical Review A 13, 2123 (1976)

    1976

  84. [92]

    Astafiev, A

    O. Astafiev, A. M. Zagoskin, A. A. Abdumalikov, Yu. A. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. S. Tsai, Resonance Fluorescence of a Single Artificial Atom, Science 327, 840 (2010)

    2010

  85. [93]

    Heitler, The Quantum Theory of Radiation, 3rd ed

    W. Heitler, The Quantum Theory of Radiation, 3rd ed. (Dover Publications, New York, 1984)

    1984

  86. [94]

    B. R. Mollow, Power Spectrum of Light Scattered by Two-Level Systems, Physical Review 188, 1969 (1969)

    1969

  87. [95]

    Jaynes and F

    E. Jaynes and F. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proceedings of the IEEE 51, 89 (1963)

    1963

  88. [96]

    Cohen-Tannoudji, J

    C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley, 1998)

    1998

  89. [97]

    Dalibard and S

    J. Dalibard and S. Reynaud, Correlation signals in res- onance fluorescence : Interpretation via photon scatter- ing amplitudes, Journal de Physique 44, 1337 (1983)

    1983

  90. [98]

    Zubizarreta Casalengua, J

    E. Zubizarreta Casalengua, J. C. L´ opez Carre˜ no, E. Del Valle, and F. P. Laussy, Structure of the har- monic oscillator in the space of n -particle Glauber cor- relators, Journal of Mathematical Physics 58, 062109 (2017)

    2017

  91. [99]

    Mandelstam and Ig

    L. Mandelstam and Ig. Tamm, The uncertainty relation between energy and time in non-relativistic quantum mechanics, in Selected Papers, Vol. IX (Springer Berlin Heidelberg, Berlin, Heidelberg, 1991) pp. 115–123

    1991

  92. [100]

    J. C. L´ opez Carre˜ no, E. Z. Casalengua, F. P. Laussy, and E. Del Valle, Joint subnatural-linewidth and single- photon emission from resonance fluorescence, Quantum Science and Technology 3, 045001 (2018)

    2018

  93. [101]

    Vivas-Via˜ na and C

    A. Vivas-Via˜ na and C. S´ anchez Mu˜ noz, Two-photon resonance fluorescence of two interacting nonidentical quantum emitters, Physical Review Research 3, 33136 (2021)

    2021

  94. [102]

    Delaubert, N

    V. Delaubert, N. Treps, C. Fabre, H. A. Bachor, and P. R´ efr´ egier, Quantum limits in image processing, EPL (Europhysics Letters) 81, 44001 (2008)

    2008

  95. [103]

    Vogel, Squeezing and anomalous moments in res- onance fluorescence, Physical Review Letters 67, 2450 24 (1991)

    W. Vogel, Squeezing and anomalous moments in res- onance fluorescence, Physical Review Letters 67, 2450 24 (1991)

    1991

  96. [104]

    Breitenbach, S

    G. Breitenbach, S. Schiller, and J. Mlynek, Measure- ment of the quantum states of squeezed light, Nature 387, 471 (1997)

    1997

  97. [105]

    C. H. H. Schulte, J. Hansom, A. E. Jones, C. Matthiesen, C. Le Gall, and M. Atat¨ ure, Quadra- ture squeezed photons from a two-level system, Nature 525, 222 (2015)

    2015

  98. [106]

    K. A. Fischer, K. M¨ uller, A. Rundquist, T. Sarmiento, A. Y. Piggott, Y. Kelaita, C. Dory, K. G. Lagoudakis, and J. Vuˇ ckovi´ c, Self-homodyne measurement of a dy- namic Mollow triplet in the solid state, Nature Photon- ics 10, 163 (2016)

    2016

  99. [107]

    C. W. Gardiner, Driving a quantum system with the output field from another driven quantum system, Phys- ical Review Letters 70, 2269 (1993)

    1993

  100. [108]

    C. W. Gardiner and A. S. Parkins, Driving atoms with light of arbitrary statistics, Physical Review A 50, 1792 (1994)

    1994

  101. [109]

    H. J. Carmichael, Quantum trajectory theory for cas- caded open systems, Physical Review Letters 70, 2273 (1993)

    1993

  102. [110]

    C. W. Gardiner and C. W. Gardiner, Stochastic Meth- ods: A Handbook for the Natural and Social Sciences, 4th ed., Springer Series in Synergetics (Springer, Berlin, 2009)

    2009

  103. [111]

    D. E. Evans, Irreducible quantum dynamical semi- groups, Communications in Mathematical Physics 54, 293 (1977)

    1977

  104. [112]

    D. E. Evans and H. Hanche-Olsen, The generators of positive semigroups, Journal of Functional Analysis 32, 207 (1979)

    1979

  105. [113]

    Sedrakyan and N

    H. Sedrakyan and N. Sedrakyan, Algebraic Inequalities, Problem Books in Mathematics (Springer International Publishing, 2018)

    2018

  106. [114]

    K. E. Cahill and R. J. Glauber, Density Operators and Quasiprobability Distributions, Physical Review 177, 1882 (1969)

    1969

  107. [115]

    F. A. M. De Oliveira, M. S. Kim, P. L. Knight, and V. Buek, Properties of displaced number states, Physi- cal Review A 41, 2645 (1990)

    1990

  108. [116]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun, Handbook of Mathe- matical Functions: With Formulas, Graphs and Mathe- matical Tables [Conference under the Auspices of the National Science Foundation and the Massachussetts Institute of Technology], unabridged, unaltered and corr. republ. of t...

    1964

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.