Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Time correlations from steady-state expectation values

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Steady-state measurements alone bound a system's correlation times

desk verdict Genuinely useful conditional bound on correlation times from steady-state data, but Eq. (7)'s condition (*) is under-characterized and the paper oversells its universality. read the letter →

arxiv 2507.08661 v1 pith:ORFRGMIH submitted 2025-07-11 quant-ph cond-mat.mes-hall

Wojciech Górecki , Simone Felicetti , Lorenzo Maccone , Roberto Di Candia This is my paper · ORCID
classification quant-phcond-mat.mes-hall
keywords steady-statecorrelationboundssecond-ordertimerelaxationquantummetrologydriven-dissipativesystemscriticalopen
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 establishes that for a broad class of Markovian open quantum systems, the relaxation time and the second-order correlation time of emitted light are lower-bounded by quantities computable entirely from steady-state expectation values and their derivatives with respect to a control parameter. The bounds follow from quantum metrology's fundamental precision limits, reinterpreted as a statement about temporal correlations: if a steady state is more sensitive to a parameter change than the uncorrelated-measurement bound allows, that excess sensitivity must be carried by temporal correlations. The authors demonstrate the bounds on a driven-dissipative resonator, where they nearly saturate the exact correlation time, and on the infinite-range dissipative Ising model, where the dynamics are otherwise intractable but the steady state is known.

What carries the argument

The central mechanism is the quantum metrology bound on signal-to-noise ratio for continuously monitored Markovian systems: the quantum Fisher information accumulated over time $t$ is bounded by $4/\gamma_0 \int_0^t \langle G_0\rangle_{t'} dt'$ for the unobserved fraction of photons. The paper treats the same physical system as coupled to an unmonitored environment (rate $\gamma_0$) and an ancilla representing measurable photons (rate $\gamma_1$), with $\gamma_0+\gamma_1=\gamma$. If the measurement outcomes were temporally uncorrelated, the SNR would grow only linearly with the number of samples; any super-linear growth forced by the bound must be supplied by the second-order correlation function. Inverting this logic yields the lower bounds on $\tau_{ss}$ and $\tau_c$. The optimization over $\gamma_1$ gives the closed-form bound of Eq. (7) when the condition $2\langle G_0\rangle_{ss}/|\partial_\omega \langle G_0\rangle_{ss}| \le \gamma$ holds, which the authors argue is typical at critical points.

What would settle it

Compute the left-hand side of Eq. (7) from the exact dynamics of a Markovian driven-dissipative system (e.g., a parametrically driven Kerr resonator) over a range of parameters where the steady-state derivative $|\partial_\omega \langle G_0\rangle_{ss}|$ is large but the condition $(*)$ is violated; if the inequality is ever found to be violated when $(*)$ holds, the claim would be falsified. Alternatively, check the bound against a numerically exact solution for a many-body model where the steady state is known but the dynamics is solvable by time-dependent variational Monte Carlo.

Watch

Extended reading notes

Core claim

The paper derives a universal relation between steady-state parameter sensitivity and two key timescales. For a Hamiltonian $H = \omega G_0 + G_1$ with $G_0 \ge 0$ and photon emission rate $\gamma\langle G_0\rangle$, the relaxation time is bounded by $\tau_{ss} \ge \frac{\gamma}{4\langle G_0\rangle_{\max}} \frac{|\partial_\omega \langle O\rangle_{ss}|^2}{\Delta^2_{ss} O}$ for any observable $O$. For the emitted field, the second-order correlation time $\tau_c := \int_{-\infty}^{+\infty} [g^{(2)}(\tau)-1]d\tau$ satisfies, under a stated condition, $\tau_c \ge \frac{1}{\langle G_0\rangle_{ss}}\left[\frac{\gamma |\partial_\omega \langle G_0\rangle_{ss}|^2}{4\langle G_0\rangle_{ss}^2} - \frac{|\partial_\omega \langle G_0\rangle_{ss}|}{\langle G_0\rangle_{ss}}\right]$. Both formulas involve only steady-state values and parameter derivatives, so they can be evaluated without solving the dynamics. The paper shows that near critical points the bound typically diverges, signaling strong bunching, and it generalizes the argument to arbitrary observables via a constant $C[\partial_\omega H, \{L_i\}]$ that depends only on the Hamiltonian perturbation and Lindblad operators.

Load-bearing premise

The headline bound on $\tau_c$ assumes the condition $2\langle G_0\rangle_{ss}/|\partial_\omega \langle G_0\rangle_{ss}| \le \gamma$, which the paper says is typically satisfied at critical points but does not systematically characterize when it fails.

Editorial extensions

If this is right

  • Experimentalists can estimate correlation times of ultrafast systems by measuring only steady-state photon flux and its derivative with respect to a tunable parameter, bypassing sub-picosecond detector resolution.
  • For many-body models whose steady state is solvable but whose dynamics are not, the bounds provide analytic constraints on relaxation and bunching timescales without solving the master equation.
  • Near quantum critical points, the divergent steady-state susceptibility automatically implies divergent correlation and relaxation times, making the connection between criticality and long-lived temporal correlations quantitative.
  • The method generalizes to autocorrelations of arbitrary observables, so the same technique can bound time-correlation properties beyond photon counting, such as spin or charge autocorrelations.
  • The bounds are universal in the sense that they do not depend on the specific form of the driving Hamiltonian $G_1$, only on its effect on the steady state.

Reading between the lines

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

  • A testable extension is to apply the bound to a driven-dissipative system where the steady state is known only numerically and compare the bound against direct Monte Carlo simulations of the dynamics; the inequality should hold for all parameters, providing a consistency check.
  • The method might be inverted: if an experiment can resolve the correlation time but not the steady-state derivative, the bound gives a nontrivial constraint on the susceptibility, effectively a thermodynamic uncertainty relation.
  • The condition $2\langle G_0\rangle_{ss}/|\partial_\omega \langle G_0\rangle_{ss}| \le \gamma$ is the regime where the optimized $\gamma_1$ is in the interior; outside it, the bound takes a different, more complicated form, but the underlying SNR inequality still holds, so a weaker bound remains available.
  • The general observable bound of Eq. (10) may be useful for non-photon observables such as order parameters in dissipative phase transitions, connecting critical metrology sensitivity to the autocorrelation time of the order parameter itself.
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

3 major / 5 minor

Summary. The paper derives lower bounds on two dynamical timescales of Markovian driven-dissipative systems: the relaxation time tau_ss and the second-order correlation time tau_c = integral(g^(2)(tau)-1)d tau. The starting point is a quantum-Fisher-information bound for Markovian noise (Eq. (2)), which the authors combine with the signal-to-noise ratio of counting monitored output photons. By splitting the total dissipation rate gamma into an unmonitored part gamma_0 and a monitored part gamma_1, they obtain Eq. (3) for tau_ss and Eq. (7) for tau_c, expressed solely through steady-state expectation values and their derivatives with respect to a parameter omega. A generalization to arbitrary observables is stated as Eq. (10). The method is benchmarked on a lossy parametric resonator, where the exact g^(2) is computed in End Matter III and the bound matches the exact scaling near criticality, and on the infinite-range dissipative transverse-field Ising model, whose steady state is known exactly but whose dynamics is not analytically tractable.

Significance. If the bounds are valid as stated, the paper provides a practical and conceptually interesting bridge: correlation times can be estimated from steady-state susceptibility data, without time-resolved detection or solving the dynamics. The parametric-resonator validation is a genuine strength, since the bound is compared with a fully analytical exact solution and is shown to be tight up to leading order in the relevant regime. The Ising example demonstrates that the method can produce nontrivial statements about a model whose dynamics are otherwise inaccessible. The derivation does not fit any free parameters: the external QFI inequalities are used to constrain the time-integrated correlations, and the examples provide concrete, checkable predictions. The main weakness is that the headline formula Eq. (7) is conditional on an uncharacterized assumption, so the advertised generality is not fully established.

major comments (3)
  1. [Main results, Eq. (7)] Eq. (7) is not a universal steady-state lower bound as the abstract implies. The optimization over gamma_1 has an interior solution gamma_1 = 2<G0>_ss/|d_omega<G0>_ss| only when condition (*) holds. As the authors note, when (*) fails the optimum moves to the boundary gamma_1=gamma, where gamma_0=0 and Eq. (4) becomes vacuous, so the method produces no nontrivial bound. The statement that (*) is 'typically satisfied' at critical points is not backed by a general criterion or by an explicit characterization of the failure region. Since a user must verify a condition involving the same steady-state susceptibility that the method is intended to exploit, the paper should present Eq. (7) as a conditional theorem, discuss the boundary case explicitly, and provide at least a criterion or an example showing when (*) fails and the bound becomes trivial.
  2. [Main results, Eq. (3)] The derivation of the relaxation-time bound identifies the estimation time t in Eq. (2) with the relaxation time tau_ss without giving an operational definition of tau_ss. If tau_ss is a hitting time at which the state exactly reaches the steady state, then Eq. (3) follows from Eq. (2) applied at t=tau_ss, but the use of <O>_ss and Delta^2_ss O requires the state to be exactly steady at that time. If tau_ss is instead intended as a dynamical timescale such as the inverse Liouvillian gap, the inequality does not follow directly. Please state precisely what Eq. (3) bounds and how tau_ss is defined; the example comparison is only at the level of scaling and does not resolve this ambiguity.
  3. [General observable of the output field, Eq. (10)] Eq. (10) is listed as one of the three main results, but its hypotheses are not stated. It is unclear what class of observables A is allowed (a system operator, an output-field operator, or both), how the constant C[d_omega H,{L_i}] is computed from the Lindblad operators, and under what conditions the steady-state autocorrelation integral is finite or the inequality holds. A reader cannot apply or assess Eq. (10) without returning to the metrology literature. The authors should either derive Eq. (10) in the End Matter or state it as a theorem with explicit conditions and a clear reference to the corresponding result in Refs. [31-33].
minor comments (5)
  1. [End Matter I, Eqs. (23)-(24)] The derivation of Eq. (5) uses gamma in place of gamma_1 in the variance formula, while Eq. (5) and the preceding text use gamma_1 for the monitored output mode. As printed, the appendix does not reproduce Eq. (5); the notation for the measured output mode should be made consistent.
  2. [Abstract and introduction] The phrase 'general lower bounds' in the abstract overstates the scope of Eq. (7), which requires condition (*). The abstract should either mention the condition or the main text should qualify the claim in the introduction.
  3. [Fig. 3 caption] The caption states that the density plot was generated using 'Eqs. (14) and (S39) of [40]'; this appears to be a typo, since Eq. (14) of the present paper is the relaxation-time bound, not the correlation-time formula plotted. It should likely refer to Eq. (19) of this paper and Eq. (S39) of Ref. [40].
  4. [Fig. 3 inset caption] The inset caption contains a duplicated word: 'calculated for for fixed values'. In addition, the claim that the variance of m converges to a finite constant in the thermodynamic limit with Delta^2_ss m approximately 0.16 is stated without derivation or citation; a brief justification would be helpful.
  5. [General setting, Eq. (8)] The role of the Lindbladian M[rho] is described ambiguously: the text first says it models the coupling to the measurement apparatus, then says it accounts for effects related to interaction with a controlled field. These two descriptions should be reconciled, since the distinction between L and M is later used to make Eq. (9) independent of M.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: Eq. (7) follows algebraically from the QFI bound (4) and the SNR formula (5), and the only self-citation (ref [33]) is not load-bearing because it is joint with independent refs [31,32].

full rationale

I walked the paper's derivation chain. The fundamental QFI bound in Eq. (2) is imported from refs [31-33]; although ref [33] is by the present authors, refs [31] and [32] are independent prior works, and the bound is stated as a published result rather than derived from the paper's own target quantities. Eq. (5) is derived in End Matter I from the output-field SNR using the definition of g(2)(tau) and an exponential-decay approximation; tau_c appears in the denominator of the SNR, so combining Eq. (4) with Eq. (5) and solving for tau_c is a legitimate inequality rearrangement, not a definitional identity. The optimization over gamma_1 is explicit (gamma_1 = min{2<G0>_ss/|partial_omega<G0>_ss|, gamma}), and Eq. (7) is exactly the resulting bound; no parameter is fitted afterward, and the examples compare against independently computed exact solutions (e.g., the Langevin solution for the parametric amplifier). The only caveat is condition (*), which the paper explicitly states; this limits the regime of validity of Eq. (7) but is not circularity. Therefore the central claims are self-contained up to the cited external metrology bound, and there is no significant circularity.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The derivation rests on the Markovian open-system framework, the specific dissipator structure that ties photon flux to ⟨G₀⟩, and the external QFI bound of refs [31-33]. No parameters are fitted to data, and no new entities are introduced. The condition (*) is an ad hoc assumption limiting the simplified formula.

assumptions (5)
  • domain assumption The system obeys a Markovian master equation dρ/dt = -i[H,ρ] + γD[ρ] with H = ωG₀ + G₁ and a unique steady state.
    This is the setting in Eq. (1); all bounds are derived within this class of systems. Uniqueness of the steady state is needed for the long-time limits.
  • domain assumption The dissipator D acts in the eigenbasis of G₀, with equally spaced levels and transitions only between neighboring levels, so the emitted photon flux equals γ⟨G₀⟩.
    Used for Eq. (23) ⟨b†b⟩ = γ⟨G₀⟩, which is essential for the SNR formula (5) and hence the τc bound (7). Many driven systems with photon emission into a bath satisfy this.
  • standard math The QFI bound QFI ≤ (4/γ₀)∫⟨G₀⟩dt' holds for the metrological scheme with both monitored and unmonitored loss, as derived in refs [31-33].
    This is the external inequality the paper builds on. It is cited, not re-derived. For the photon-monitoring case, the split γ = γ₀ + γ₁ is argued to leave the bound valid with γ₀.
  • ad hoc to paper Condition (*): 2⟨G₀⟩_ss/|∂ω⟨G₀⟩_ss| ≤ γ.
    Introduced in the optimization over γ₁ to obtain the simplified Eq. (7). The paper says it is typically satisfied at critical points, but gives no general characterization. The bound outside this branch is not written down.
  • domain assumption g(2)(τ)-1 decays exponentially with rate at least λ_min, the smallest real part of the Liouvillian eigenvalue.
    Used in End Matter I, Eq. (25), to replace the double integral over the measurement window by t·τc. Holds for finite-dimensional Lindbladians with a unique steady state, but is an assumption on the spectrum.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Time correlations from steady-state expectation values." pith.science (2026). https://pith.science/paper/ORFRGMIH

@misc{pith2026250708661,
  author       = {Pith},
  title        = {Pith review of: Time correlations from steady-state expectation values},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ORFRGMIH}},
  note         = {Machine review of arXiv:2507.08661}
}
read the original abstract

Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a control parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to experimentally characterize ultrafast systems, and to theoretically analyze many-body models with dynamics that are analytically or numerically hard.

Figures

Figures reproduced from arXiv: 2507.08661 by the authors.

Figure 1
Figure 1. FIG. 1. We consider a general open quantum system coupled to a [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic representation of an open quantum system driven [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Density plot of the value of the lower bound for output pho [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Since the function [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Quantum metrology through spectral measurements in quantum optics

    quant-ph 2025-09 conditional novelty 7.0 of 10

    Frequency-resolved photon counting with a coherently displaced local oscillator can saturate the quantum Fisher information for parameters of a driven two-level emitter, and two-color photon correlations give up to a ...

Reference graph

Works this paper leans on

51 extracted references · 35 canonical work pages · cited by 1 Pith paper

  1. [33]

    G ´orecki, F

    W. G ´orecki, F. Albarelli, S. Felicetti, R. Di Candia, and L. Mac- cone, Interplay between time and energy in bosonic noisy quan- tum metrology, PRX Quantum 6, 020351 (2025)

    work page 2025

  2. [1]

    Mandel and E

    L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge university press, 1995)

    1995

  3. [2]

    A. H. Kiilerich and K. Mølmer, Estimation of atomic interac- tion parameters by photon counting, Phys. Rev. A 89, 052110 (2014)

    work page 2014

  4. [3]

    A. H. Kiilerich and K. Mølmer, Bayesian parameter estimation by continuous homodyne detection, Phys. Rev. A 94, 032103 (2016)

    work page 2016

  5. [4]

    D. Yang, S. F. Huelga, and M. B. Plenio, Efficient information retrieval for sensing via continuous measurement, Phys. Rev. X 13, 031012 (2023)

    work page 2023

  6. [5]

    Radaelli, J

    M. Radaelli, J. A. Smiga, G. T. Landi, and F. C. Binder, Pa- rameter estimation for quantum jump unraveling, arXiv preprint arXiv:2402.06556 (2024)

    work page arXiv 2024

  7. [6]

    Mattes, A

    R. Mattes, A. Cabot, F. Carollo, and I. Lesanovsky, De- signing open spin-boson models for enabling quantum en- hanced sensing through classical measurements, arXiv preprint arXiv:2505.08756 (2025)

    arXiv 2025

  8. [7]

    Cardy, Scaling and renormalization in statistical physics , V ol

    J. Cardy, Scaling and renormalization in statistical physics , V ol. 5 (Cambridge university press, 1996)

    1996

Show all 51 references
  1. [8]

    Sachdev, Quantum Phase Transitions , 2nd ed

    S. Sachdev, Quantum Phase Transitions , 2nd ed. (Cambridge University Press, Cambridge, 2011)

    2011

  2. [9]

    Arakawa and M

    Y . Arakawa and M. J. Holmes, Progress in quantum-dot single photon sources for quantum information technologies: A broad spectrum overview, Appl. Phys. Rev.7 (2020)

    2020

  3. [10]

    Toninelli, I

    C. Toninelli, I. Gerhardt, A. Clark, A. Reserbat-Plantey, S. G ¨otzinger, Z. Ristanovi´c, M. Colautti, P. Lombardi, K. Ma- jor, I. Deperasi ´nska, et al., Single organic molecules for pho- tonic quantum technologies, Nat. Mater. 20, 1615 (2021)

    2021

  4. [11]

    M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, The nitrogen-vacancy colour centre in diamond, Phys. Rep. 528, 1 (2013). 6

    2013

  5. [12]

    Salem, M

    R. Salem, M. A. Foster, and A. L. Gaeta, Application of space– time duality to ultrahigh-speed optical signal processing, Ad- vances in Optics and Photonics 5, 274 (2013)

    2013

  6. [13]

    R. H. Hadfield, J. Leach, F. Fleming, D. J. Paul, C. H. Tan, J. S. Ng, R. K. Henderson, and G. S. Buller, Single-photon detection for long-range imaging and sensing, Optica 10, 1124 (2023)

    2023

  7. [14]

    Horoshko, S

    D. Horoshko, S. Srivastava, B. Brecht, M. Kolobov, et al. , Time-resolved second-order autocorrelation function of para- metric downconversion, arXiv preprint arXiv:2502.07691 (2025)

    2025 arXiv

  8. [15]

    Breuer, F

    H.-P. Breuer, F. Petruccione, et al., The theory of open quantum systems (Oxford University Press on Demand, 2002)

    2002

  9. [16]

    Kubo, The fluctuation-dissipation theorem, Rep

    R. Kubo, The fluctuation-dissipation theorem, Rep. Prog. Phys. 29, 255 (1966)

    1966

  10. [17]

    V . V . Albert, B. Bradlyn, M. Fraas, and L. Jiang, Geometry and response of Lindbladians, Phys. Rev. X 6, 041031 (2016)

    2016

  11. [18]

    Minganti, A

    F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spectral theory of liouvillians for dissipative phase transitions, Phys. Rev. A98, 042118 (2018)

    2018

  12. [19]

    Kamenev, Field theory of non-equilibrium systems (Cam- bridge University Press, 2023)

    A. Kamenev, Field theory of non-equilibrium systems (Cam- bridge University Press, 2023)

    2023

  13. [20]

    L. M. Sieberer, M. Buchhold, and S. Diehl, Keldysh field theory for driven open quantum systems, Rep. Prog. Phys. 79, 096001 (2016)

    2016

  14. [21]

    X. H. Zhang and H. U. Baranger, Driven-dissipative phase tran- sition in a Kerr oscillator: From semiclassical PT symmetry to quantum fluctuations, Phys. Rev. A 103, 033711 (2021)

    2021

  15. [22]

    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)

    2008

  16. [23]

    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)

    2011

  17. [24]

    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)

    2012

  18. [25]

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

    2014 arXiv

  19. [26]

    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)

    2014

  20. [27]

    Zhou and L

    S. Zhou and L. Jiang, Asymptotic theory of quantum channel estimation, PRX Quantum 2, 010343 (2021)

    2021

  21. [28]

    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)

    2023

  22. [29]

    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)

    2018

  23. [30]

    A. Das, W. G ´orecki, and R. Demkowicz-Dobrza´nski, Universal time scalings of sensitivity in Markovian quantum metrology, Phys. Rev. A 111, L020403 (2025)

    2025

  24. [31]

    Demkowicz-Dobrza ´nski, J

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

    2017

  25. [32]

    Wan and R

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

    2022

  26. [34]

    Zanardi and N

    P. Zanardi and N. Paunkovi´c, Ground state overlap and quantum phase transitions, Phys. Rev. E 74, 031123 (2006)

    2006

  27. [35]

    M. M. Rams, P. Sierant, O. Dutta, P. Horodecki, and J. Za- krzewski, At the limits of criticality-based quantum metrology: Apparent super-Heisenberg scaling revisited, Phys. Rev. X 8, 021022 (2018)

    2018

  28. [36]

    Garbe, M

    L. Garbe, M. Bina, A. Keller, M. G. A. Paris, and S. Felicetti, Critical quantum metrology with a finite-component quantum phase transition, Phys. Rev. Lett. 124, 120504 (2020)

    2020

  29. [37]

    Beaulieu, F

    G. Beaulieu, F. Minganti, S. Frasca, V . Savona, S. Felicetti, R. Di Candia, and P. Scarlino, Observation of first-and second- order dissipative phase transitions in a two-photon driven Kerr resonator, Nat. Comm. 16, 1 (2025)

    2025

  30. [38]

    Beaulieu, F

    G. Beaulieu, F. Minganti, S. Frasca, M. Scigliuzzo, S. Felicetti, R. Di Candia, and P. Scarlino, Criticality-enhanced quantum sensing with a parametric superconducting resonator, PRX Quantum 6, 020301 (2025)

    2025

  31. [39]

    Alushi, W

    U. Alushi, W. G ´orecki, S. Felicetti, and R. Di Candia, Optimal- ity and Noise Resilience of Critical Quantum Sensing, Phys. Rev. Lett. 133, 040801 (2024)

    2024

  32. [40]

    Roberts and A

    D. Roberts and A. A. Clerk, Exact solution of the infinite-range dissipative transverse-field Ising model, Phys. Rev. Lett. 131, 190403 (2023)

    2023

  33. [41]

    Giovannetti, S

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

    2006

  34. [42]

    De Pasquale, D

    A. De Pasquale, D. Rossini, P. Facchi, and V . Giovannetti, Quantum parameter estimation affected by unitary disturbance, Phys. Rev. A 88, 052117 (2013)

    2013

  35. [43]

    The operator norm of a matrix is its largest singular value

  36. [44]

    Navarrete-Benlloch, Introduction to quantum optics, arXiv preprint arXiv:2203.13206 (2022)

    C. Navarrete-Benlloch, Introduction to quantum optics, arXiv preprint arXiv:2203.13206 (2022)

    2022 arXiv

  37. [45]

    D. F. Walls and G. J. Milburn, Quantum optics (Springer Sci- ence & Business Media, 2007)

    2007

  38. [46]

    Yamamoto, K

    T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki, W. D. Oliver, Y . Nakamura, and J. S. Tsai, Flux- driven Josephson parametric amplifier, Appl. Phys. Lett. 93, 042510 (2008)

    2008

  39. [47]

    Zhong, E

    L. Zhong, E. P. Menzel, R. Di Candia, P. Eder, M. Ihmig, A. Baust, M. Haeberlein, E. Hoffmann, K. Inomata, T. Ya- mamoto, Y . Nakamura, E. Solano, F. Deppe, A. Marx, and R. Gross, Squeezing with a flux-driven Josephson parametric amplifier, New J. Phys. 15, 125013 (2013)

    2013

  40. [48]

    N. E. Frattini, R. G. Corti ˜nas, J. Venkatraman, X. Xiao, Q. Su, C. U. Lei, B. J. Chapman, V . R. Joshi, S. Girvin, R. J. Schoelkopf, et al., Observation of pairwise level degeneracies and the quantum regime of the Arrhenius law in a double-well parametric oscillator, Phys. R...

    2024

  41. [49]

    Krantz, Y

    P. Krantz, Y . Reshitnyk, W. Wustmann, J. Bylander, S. Gus- tavsseon, W. D. Oliver, T. Duty, V . Shumeiko, and P. Delsing, Investigation of nonlinear effects in Josephson parametric os- cillators used in circuit quantum electrodynamics, New J. Phys. 15, 105002 (2013)

    2013

  42. [50]

    Note, that for the investigated range of N up to 212 this value still varies by up to 10%

  43. [51]

    Kurdzialek, F

    S. Kurdzialek, F. Albarelli, and R. Demkowicz-Dobrzanski, Universal bounds for quantum metrology in the presence of cor- related noise, arXiv preprint arXiv:2410.01881 (2024). 7 END MA TTER I. DERIV A TION OF EQ. (5) We consider the observable O = Z t 0 b†(t′)b(t′)dt′, (20) wh...

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.