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REVIEW 3 major objections 6 minor 2 cited by

Detector Correlations and Null Tests of the Coherent State Hypothesis

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Cross-correlating two resonant detectors gives a vacuum-noise-free null test of the coherent state hypothesis.

desk verdict Correct and clean formal null-test results; the missing statistical power analysis is the gap between a theorem and a feasible experiment. read the letter →

arxiv 2508.03367 v1 pith:MPZ37RIG submitted 2025-08-05 quant-ph gr-qc

Sreenath K. Manikandan , Frank Wilczek This is my paper · ORCID
classification quant-phgr-qc PACS 04.30.-w03.65.Ta42.50.Ar
keywords coherentstatehypothesisgravitationalradiationresonantmassdetectorscross-correlationsMandelQparameterquadraturesqueezingsecond-ordercoherencenulltests
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

The paper proposes a way to test whether a radiation field, in particular gravitational radiation, is in a coherent state by measuring cross-correlations between two resonant-mass detectors that couple to the same field mode. Its central claim is that for coherent states these cross-correlations vanish exactly, so any statistically significant non-zero value rules out the coherent state hypothesis without needing to subtract vacuum noise. The single-detector vacuum noise cancels in the difference between the joint and product expectations, which is why these are called null tests free of quantum noise. Nonzero correlations are then signatures of non-classical structure such as number or phase squeezing, and the ratio of joint to product click counts directly estimates the second-order coherence function $g^{(2)}(0)$. The authors argue that the required parameter regime, $\gamma_0\Delta t \langle a^{\dagger}a\rangle \sim O(1)$, is achievable with proposed resonant-mass gravitational-wave detectors in the kilohertz band.

What carries the argument

The load-bearing object is the joint state after interaction, Eq. (4): $\rho' \approx \int d^2\alpha\, P(\alpha)|\alpha\rangle\langle\alpha| \otimes |-i\alpha\sqrt{\gamma_0\Delta t}\rangle\langle -i\alpha\sqrt{\gamma_0\Delta t}|_1 \otimes |-i\alpha\sqrt{\gamma_0\Delta t}\rangle\langle -i\alpha\sqrt{\gamma_0\Delta t}|_2$. It is obtained by diagonalizing the field in coherent states via the $P$-representation and using the fact that each detector, starting in vacuum, is displaced by the same amplitude $-i\alpha\sqrt{\gamma_0\Delta t}$ when $\gamma_0\Delta t\ll 1$. This common displacement makes all connected detector correlators proportional to connected moments of $\alpha$, and for a coherent field $P(\alpha)=\delta^{(2)}(\alpha-\alpha_0)$ those moments vanish. The machinery therefore converts quantum-state structure into ordinary $c$-number statistics of the $P$-function, and the null tests are just statements that a delta-peaked $P$-function has no connected moments.

What would settle it

The sharpest falsifier is a controlled measurement: point two identical ground-state resonant detectors at a source believed to be coherent and accumulate joint click and quadrature statistics. If the connected cross-correlators $\langle N_1N_2\rangle - \langle N_1\rangle\langle N_2\rangle$, $\langle x_1x_2\rangle - \langle x_1\rangle\langle x_2\rangle$, or $\langle\mathrm{Re}\,\beta_1\mathrm{Re}\,\beta_2\rangle - \langle\mathrm{Re}\,\beta_1\rangle\langle\mathrm{Re}\,\beta_2\rangle$ come out statistically nonzero with the predicted $\gamma_0\Delta t$ scaling, the coherent state hypothesis for that mode is wrong; conversely, a tabletop experiment with a known coherent laser field must reproduce zero within counting statistics, and any unexplained offset would expose a failure of the single-mode assumption.

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Extended reading notes

Core claim

The central claim is that the connected cross-correlations of two initially uncorrelated resonant detectors are exact null tests of the coherent state hypothesis. For click detectors the authors derive $\langle N_1 N_2\rangle - \langle N_1\rangle \langle N_2\rangle = (\gamma_0\Delta t)^2 Q\langle a^{\dagger}a\rangle$, which vanishes for coherent states because Mandel's $Q$ parameter is zero; for homodyne readouts they obtain $\langle x_1 x_2\rangle - \langle x_1\rangle\langle x_2\rangle = x_{01} x_{02}\gamma_0\Delta t (\langle(\Delta \hat{P})^2\rangle - \tfrac{1}{2})$, and for heterodyne readouts $\langle \mathrm{Re}\,\beta_1\,\mathrm{Re}\,\beta_2\rangle - \langle \mathrm{Re}\,\beta_1\rangle\langle \mathrm{Re}\,\beta_2\rangle = \tfrac{1}{2}\gamma_0\Delta t(\langle(\Delta \hat{P})^2\rangle - \tfrac{1}{2})$, both vanishing because coherent states have quadrature variance $\tfrac{1}{2}$. A further connected correlator, $\langle \beta_1^* \beta_2\rangle - \langle \beta_1^*\rangle\langle \beta_2\rangle = \gamma_0\Delta t(\langle a^{\dagger}a\rangle - \langle a^{\dagger}\rangle\langle a\rangle)$, also vanishes for coherent states. The single-mode, small-coupling approximation leaves the field mode nearly unchanged while each detector is displaced by $-i\alpha\sqrt{\gamma_0\Delta t}$, and every null follows from the fact that moments of $\alpha$ factor for a coherent $P(\alpha)$. No vacuum term survives in the differences, which is why the tests are described as free of quantum noise.

Load-bearing premise

The argument's load-bearing premise is that the two detectors are identical, start in their ground states, and couple to exactly the same single mode of the field with no relative time delay or decoherence, so both detector states are displaced by the same amplitude; real gravitational radiation contains many modes, and any multimode mixing or phase mismatch would alter the correlations and could obscure the exact null.

Editorial extensions

If this is right

  • A statistically significant non-zero value of $\langle N_1 N_2\rangle - \langle N_1\rangle\langle N_2\rangle$ would directly falsify the coherent state hypothesis for the probed radiation mode without any vacuum-noise subtraction.
  • The ratio $R = \langle N_1 N_2\rangle/(\langle N_1\rangle\langle N_2\rangle)$ estimates $g^{(2)}(0)$, and it can be cross-checked against the single-detector expression $R \approx 2P_2 P_0/P_1^2$, offering reduced sampling error.
  • Joint homodyne or heterodyne readouts give access to $\langle(\Delta \hat{P})^2\rangle - 1/2$, so positive deviations reveal number-like states and negative deviations reveal phase squeezing, complementing click measurements.
  • The connected correlator $\langle\beta_1^*\beta_2\rangle - \langle\beta_1^*\rangle\langle\beta_2\rangle = \gamma_0\Delta t(\langle a^{\dagger}a\rangle - \langle a^{\dagger}\rangle\langle a\rangle)$ provides a null test that is especially sensitive to states such as Fock and thermal states whose average heterodyne signal vanishes.
  • The parameter condition $\gamma_0\Delta t\langle a^{\dagger}a\rangle \sim O(1)$ can be met by kilohertz gravitational radiation with LIGO-like energy densities, so the tests are within reach of proposed resonant-mass detectors.

Reading between the lines

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

  • An implicit extension the paper leaves open is a multimode analysis: real gravitational-wave sources emit a continuum of modes, and mixing across modes could produce apparent nonzero correlations even for a coherent overall field, so a practical null test would need mode filtering or design around a dominant mode.
  • The same connected-correlator logic could be tested in the laboratory with optical or microwave fields, where the detector coupling is not minuscule, to validate the formalism before gravitational-wave application.
  • Combining click and homodyne null tests could discriminate states that are indistinguishable in a single observable: a Fock state can show a near-null click correlator at small $\gamma_0\Delta t$ while producing a large homodyne correlator, so the two tests are complementary probes of non-coherent structure.
  • A positive null-test signal would show the radiation field is not coherent, but it would not by itself prove that individual gravitons were detected; it establishes that a quantum, non-classical description is required.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This paper proposes null tests of the coherent-state hypothesis for gravitational radiation using cross-correlations between two resonant mass detectors. Under a model in which two identical, initially vacuum detectors interact weakly with a common single mode of the radiation field, the authors derive three cross-correlators: click counts (Eq. 9), homodyne quadratures (Eq. 15), and heterodyne readouts (Eq. 19). Each vanishes when the field is in a coherent state, and the authors argue that these tests are free of vacuum and measurement noise in the mean. The formal derivations are correct within the stated small-gamma0-delta-t approximation, and the paper connects the click correlator to the second-order coherence function g^(2)(0).

Significance. If the central claims hold, this is a valuable theoretical proposal: it turns a fundamental question about the quantum nature of gravitational radiation into a concrete cross-detector measurement with no fitted parameters. The derivations are self-contained, the weak-coupling approximation is explicitly stated, and the cancellation for coherent states is robust to variations such as different detector couplings or timing, because a coherent field leaves the two detectors in a product of coherent states. The proposed relation to g^(2)(0) and the complementarity among click, homodyne, and heterodyne tests are useful contributions. However, the manuscript currently overstates the practical reach of the tests: it provides no statistical power analysis to support the feasibility claim in the Conclusions, and it uses 'free of vacuum noise' in a way that is true only for the mean of the cross-correlator, not for finite-sample estimators. The interpretive claim that a nonzero cross-correlator demonstrates the inadequacy of a classical description is also too strong, since positive-P (classical) states such as thermal states can give nonzero Mandel Q.

major comments (3)
  1. [Section V (Conclusions)] The statement that 'the required parameter values for resonant mass detectors are such that our tests could be feasible' is not supported by any noise or statistical-power estimate. Equations (9), (15), and (19) give the mean of the cross-correlator, but a null test is performed by comparing a finite-sample estimate of that mean with its uncertainty. For the click detector, when the field is coherent, N1 and N2 are independent Poisson variables with mean lambda = gamma0 delta-t <a^dag a>, so the sample covariance across M runs has variance of order lambda^2/M; the signal for super-Poissonian states is (gamma0 delta-t)^2 Q <a^dag a> = (gamma0 delta-t) lambda Q, so the required number of runs scales as M ~ 1/(gamma0 delta-t Q)^2 unless Q is itself of order <a^dag a>. The homodyne and heterodyne estimators are likewise subject to sampling noise that includes the individual detectors' vacuum fluctuations even though those fluctuations cancel in the mean. Without this analysis, the feasibility claim in the Conclusions is unsubstantiated.
  2. [Abstract; Sections III and V] The phrase 'free of vacuum (quantum) noise' is correct only for the expectation value of the cross-correlator, not for the measurement process. In the homodyne case, each detector readout x_i contains a vacuum fluctuation of variance x0i^2, and although these fluctuations cancel in the mean of x1 x2 - <x1><x2>, they contribute to the variance of any finite-sample estimate of that quantity. The same applies to heterodyne readouts and to the click-count correlator. The abstract and Section V should be reworded to say that the mean cross-correlator is insensitive to vacuum and measurement noise, and the finite-sample noise budget should be stated explicitly.
  3. [Introduction and Section V (last paragraph)] The paper equates 'violation of the coherent state hypothesis' with demonstrating 'the inadequacy of a classical or semi-classical description,' but the proposed tests do not certify nonclassicality. The click correlator in Eq. (9) is proportional to the Mandel Q parameter, which can be positive for states with a positive P function, e.g., a thermal state or a phase-randomized coherent state. Such states are not coherent states, but they admit a classical stochastic description in the Glauber-Sudarshan sense. A nonzero cross-correlator therefore rules out a single coherent state, but it does not by itself rule out a classical stochastic field. The authors should either restrict the claim to 'not a coherent state' or add a test that can positively certify nonclassicality.
minor comments (6)
  1. [Section II, Eq. (3)] For nonclassical field states, the diagonal P function is a generalized (singular) distribution; the formal integrals over P(alpha) should be understood distributionally, and it would be helpful to state this explicitly.
  2. [Section III, Eq. (15)] The step from <Im(alpha)^2> - <Im(alpha)>^2 to (1/2)(<(Delta P)^2> - 1/2) is not shown; please include the operator-ordering identity <alpha|P^2|alpha> = 2(Im alpha)^2 + 1/2, or an equivalent derivation.
  3. [Section II, Eq. (11)] The relation R = 2 P2 P0 / P1^2 is stated without derivation or a definition of P0, P1, P2; please define these quantities and either derive the relation or cite the exact equation from Ref. [3].
  4. [Section IV, Eq. (20)] The extension to cross-correlators involving beta* and beta is stated without derivation; a brief outline of the calculation would improve readability.
  5. [Throughout] There are several typographical and grammatical issues: 'frequncy' in Section II, 'for a genetic state' in Appendix A, and the phrase 'governed by are the speed of sound' in the Introduction. These should be corrected.
  6. [References] Reference [10] lists volume 0 in the journal citation; please update it to the correct volume and page numbers.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the null-test correlations are derived from the stated model and standard coherent-state identities, not from fitted parameters or self-citations.

full rationale

The derivation chain is self-contained. The interaction Hamiltonian (Eqs. 1–2) and initial product state (Eq. 3) are stated explicitly, and Appendix A computes the evolved joint state (Eqs. A5–A7) by direct unitary transformation rather than importing the null result. The cross-correlators in Eqs. (9), (15), (19), and (20) are then evaluated as expectation values and vanish for coherent states because Q = 0 and ⟨(ΔP)^2⟩ = 1/2, both standard coherent-state identities. No parameter is fitted to data; γ0 is a fixed spontaneous-emission rate, and the small-γ0Δt approximation is justified by the stated physical regime. Self-citations to Refs. [3,10,17] supply the detector model and earlier context, but the model is restated and re-derived here, and the null-test claim does not reduce to those citations. The Conclusion's feasibility remark ('could be feasible') is not supported by a statistical power analysis, but that is a completeness/correctness limitation, not a circular step.

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

The paper introduces no free parameters and no new entities. Its central claim rests on standard quantum optics and a specific detector model borrowed from prior work, plus several idealizations about single-mode coupling, ground-state preparation, and decoherence-free evolution.

assumptions (5)
  • domain assumption The gravitational field state admits a P-representation with a well-defined P(α).
    Used throughout to express expectation values of normally ordered operators; relies on the optical equivalence theorem (Refs [1,2]).
  • domain assumption The interaction between each detector and the field is a beamsplitter Hamiltonian (Eqs. 1-2) with equal coupling √(γ0Δt), and the detectors are identical and initialized in vacuum.
    This is the detector model from prior work (Ref [3]); it postulates a specific form of the graviton-detector coupling.
  • domain assumption The small-parameter approximation γ0Δt << 1 justifies truncating the exact evolution (Appendix A) to the leading-order displacement (Eq. 4).
    The authors state this approximation is valid for resonant mass detectors; it is used to derive all subsequent formulas.
  • domain assumption The two detectors couple to exactly the same single mode of the field with no time delay.
    The paper assumes a common single mode, stated in Section II; multimode or timing effects could wash out correlations.
  • domain assumption The detectors are prepared in their ground states and do not decohere during the interaction.
    Initial state in Eq. (3) is |0> for both detectors; this is a strong practical assumption for macroscopic resonant masses.

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Cite this review

Pith. "Pith review of Detector Correlations and Null Tests of the Coherent State Hypothesis." pith.science (2026). https://pith.science/paper/MPZ37RIG

@misc{pith2026250803367,
  author       = {Pith},
  title        = {Pith review of: Detector Correlations and Null Tests of the Coherent State Hypothesis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MPZ37RIG}},
  note         = {Machine review of arXiv:2508.03367}
}
read the original abstract

We discuss the statistics of correlations between two resonant detectors. We show that this allows simple null tests of the coherent state hypothesis, free of vacuum (quantum) noise. Complementary aspects of the radiation field, {\it e.g.}, squeezing in number or phase, can be revealed through appropriate detection strategies.

Discussion (0). Continue with ORCID to comment.

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Reference graph

Works this paper leans on

29 extracted references · 15 canonical work pages · cited by 2 Pith papers

  1. [1]

    Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,

    E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963)

    work page 1963

  2. [2]

    Coherent and incoherent states of the radiation field,

    Roy J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963)

    1963

  3. [3]

    Testing the coherent-state description of radiation fields,

    Sreenath K. Manikandan and Frank Wilczek, “Testing the coherent-state description of radiation fields,” Phys. Rev. A 111, 033705 (2025)

    2025

  4. [4]

    Signatures of the quantization of gravity at gravitational wave detectors,

    Maulik Parikh, Frank Wilczek, and George Zahariade, “Signatures of the quantization of gravity at gravitational wave detectors,” Phys. Rev. D 104, 046021 (2021)

    2021

  5. [5]

    Quantum mechanics of gravitational waves,

    Maulik Parikh, Frank Wilczek, and George Zahariade, “Quantum mechanics of gravitational waves,” Phys. Rev. Lett. 127, 081602 (2021)

    work page 2021

  6. [6]

    The noise of gravitons,

    Maulik Parikh, Frank Wilczek, and George Zahariade, “The noise of gravitons,” International Journal of Modern Physics D 29, 2042001 (2020)

    2020

  7. [7]

    Quantum effects in gravity waves,

    Thiago Guerreiro, “Quantum effects in gravity waves,” Classical and Quantum Gravity 37, 155001 (2020), publisher: IOP Publishing

    work page 2020

  8. [8]

    Quantum signatures in nonlinear gravitational waves,

    Thiago Guerreiro, Francesco Coradeschi, Antonia Micol Frassino, Jennifer Rittenhouse West, and En- rico Junior Schioppa, “Quantum signatures in nonlinear gravitational waves,” Quantum 6, 879 (2022)

    work page 2022

Show all 29 references
  1. [9]

    Nonlinearities in Black Hole Ringdowns and the Quantization of Gravity,

    Thiago Guerreiro, “Nonlinearities in Black Hole Ringdowns and the Quantization of Gravity,” (2023), arXiv:2306.09974 [gr-qc]. 10

    2023 arXiv

  2. [10]

    Probing quantum structure in gravita- tional radiation,

    Sreenath K. Manikandan and Frank Wilczek, “Probing quantum structure in gravita- tional radiation,” International Journal of Modern Physics D 0, 2543001 (2025), eprint: https://doi.org/10.1142/S0218271825430011

    2025 doi

  3. [11]

    Detecting single gravi- tons with quantum sensing,

    Germain Tobar, Sreenath K. Manikandan, Thomas Beitel, and Igor Pikovski, “Detecting single gravi- tons with quantum sensing,” Nature Communications 15, 7229 (2024), publisher: Nature Publishing Group

    2024

  4. [12]

    Detecting kHz gravitons from a neutron star merger with a multi-mode resonant mass detector,

    Germain Tobar, Igor Pikovski, and Michael E Tobar, “Detecting kHz gravitons from a neutron star merger with a multi-mode resonant mass detector,” Classical and Quantum Gravity 42, 055017 (2025), publisher: IOP Publishing

    2025

  5. [13]

    Wave-particle duality of gravitational radiation,

    Hudson A. Loughlin, Germain Tobar, Evan D. Hall, and Vivishek Sudhir, “Wave-particle duality of gravitational radiation,” (2025), arXiv:2504.03527 [quant-ph]

    2025

  6. [14]

    Graviton detection and the quantization of gravity,

    Daniel Carney, Valerie Domcke, and Nicholas L. Rodd, “Graviton detection and the quantization of gravity,” Phys. Rev. D 109, 044009 (2024)

    2024

  7. [15]

    Comments on graviton detection,

    Daniel Carney, “Comments on graviton detection,” (2024), arXiv:2408.00094 [gr-qc, physics:hep-ph, physics:hep-th, physics:quant-ph]

    2024

  8. [16]

    Stimulated absorption of single gravitons: First light on quantum gravity,

    Victoria Shenderov, Mark Suppiah, Thomas Beitel, Germain Tobar, Sreenath K. Manikandan, and Igor Pikovski, “Stimulated absorption of single gravitons: First light on quantum gravity,” (2024), arXiv:2407.11929 [gr-qc, physics:hep-th, physics:quant-ph]

    2024

  9. [17]

    Complementary Probes of Gravitational Radiation States,

    Sreenath K. Manikandan and Frank Wilczek, “Complementary Probes of Gravitational Radiation States,” (2025), arXiv:2505.11422 [gr-qc]

    2025 arXiv

  10. [18]

    LXXIV. A new type of interferometer for use in radio astronomy,

    R. Hanbury Brown and R.Q. Twiss, “LXXIV. A new type of interferometer for use in radio astronomy,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science45, 663–682 (1954), publisher: Taylor & Francis eprint: https://doi.org/10.1080/14786440708520475

    1954 doi

  11. [19]

    Correlation between Photons in two Coherent Beams of Light,

    R. Hanbury Brown and R. Q. Twiss, “Correlation between Photons in two Coherent Beams of Light,” Nature 177, 27–29 (1956), publisher: Nature Publishing Group

    1956

  12. [20]

    A Test of a New Type of Stellar Interferometer on Sirius,

    R. Hanbury Brown and R. Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046–1048 (1956), publisher: Nature Publishing Group

    1956

  13. [21]

    Quantum-gravitational noise correlation in nearby detectors,

    Maulik Parikh and Francesco Setti, “Quantum-gravitational noise correlation in nearby detectors,” Phys. Rev. D 111, 046004 (2025)

    2025

  14. [22]

    On the Simultaneous Measurement of a Pair of Con- jugate Observables,

    E. Arthurs and J. L. Kelly, “On the Simultaneous Measurement of a Pair of Con- jugate Observables,” Bell System Technical Journal 44, 725–729 (1965), eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/j.1538-7305.1965.tb01684.x

    1965

  15. [23]

    Squeezed Light,

    R. Loudon and P. L. Knight, “Squeezed Light,” Journal of Modern Optics34, 709–759 (1987), publisher: Taylor & Francis eprint: https://doi.org/10.1080/09500348714550721

    1987 doi

  16. [24]

    Introduction to quantum noise, measurement, and amplification,

    A. A. Clerk, M. H. Devoret, S. M. Girvin, Florian Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Reviews of Modern Physics 82, 1155–1208 (2010), publisher: American Physical Society. 11

    2010

  17. [25]

    Quantum limits on noise in linear amplifiers,

    Carlton M. Caves, “Quantum limits on noise in linear amplifiers,” Physical Review D 26, 1817–1839 (1982), publisher: American Physical Society

    1982

  18. [26]

    Quantum limits on phase- preserving linear amplifiers,

    Carlton M. Caves, Joshua Combes, Zhang Jiang, and Shashank Pandey, “Quantum limits on phase- preserving linear amplifiers,” Physical Review A 86, 063802 (2012), publisher: American Physical Society

    2012

  19. [27]

    Phase-preserving amplification near the quantum limit with a Josephson ring modulator,

    N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, “Phase-preserving amplification near the quantum limit with a Josephson ring modulator,” Nature 465, 64–68 (2010), number: 7294 Publ...

    2010

  20. [28]

    Quantum Noise in Linear Amplifiers,

    H. A. Haus and J. A. Mullen, “Quantum Noise in Linear Amplifiers,” Physical Review 128, 2407–2413 (1962), publisher: American Physical Society

    1962

  21. [29]

    Efficiently fueling a quantum engine with incompatible measurements,

    Sreenath K. Manikandan, Cyril Elouard, Kater W. Murch, Alexia Auff` eves, and Andrew N. Jordan, “Efficiently fueling a quantum engine with incompatible measurements,” Phys. Rev. E 105, 044137 (2022)

    2022

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