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REVIEW 3 major objections 6 minor 52 references

Measurement-induced entanglement entropy of gravitational wave detections

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Coincident gravitational wave detections should show measurement-induced entanglement entropy of order a few percent of the interacting graviton number, a potentially observable non-classicality signature.

desk verdict A correct entropy calculation for an arbitrary Gaussian ansatz; the few-percent 'signature' is not derived from detector physics. read the letter →

arxiv 2411.15632 v1 pith:L4VFQNNW submitted 2024-11-23 gr-qc

Preston Jones , Quentin G. Bailey , Andri Gretarsson , Edward Poon This is my paper · ORCID
classification gr-qc PACS 04.30.Nk04.30.Tv04.40.Dg04.62.+v11.15.Kc95.55.Ym
keywords gravitationalwavesgravitonentanglemententropymeasurement-inducedbipartitedetectionnon-classicalityintensity-correlationinterferometryquantumgravity
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 aims to show that gravitational radiation can be probed for quantum character without detecting single gravitons, which it takes to be physically impossible. It models a pair of coincident detectors as a bipartite system entangled by the measurement of indistinguishable gravitons with overlapping state functions, and computes the entanglement entropy of either detector subsystem from a fixed-total-number Gaussian state. The central result is that the normalized entanglement entropy, $S_A / \bar{n}$, is on the order of a few percent of the mean number of gravitons interacting with the detectors, large enough to be potentially discernible from noise. If this is correct, existing and future multiple-detector gravitational wave observatories could access a new signature of non-classicality, sidestepping the extremely low detector efficiency that blocks single-graviton detection.

What carries the argument

The central object is a pure bipartite number state for the two detectors, $|\varphi_n\rangle_g = N_g \sum_{k=0}^{n} e^{-(k-\bar{n})^2/4\sigma^2} e^{i\varphi_k} |k\rangle_A |n-k\rangle_B$, with $\sigma^2 = \bar{n}$ and $n = 2\bar{n}$; its Schmidt coefficients give the reduced density matrix of either detector. The argument's engine is the asymptotic evaluation of the entanglement entropy from Eq. (12): viewing the Gaussian sum as a Riemann sum yields $S_A \sim \tfrac{1}{2}\ln(2\pi e \bar{n})$. This identity converts the physical picture, gravitons entangling two detectors during measurement, into a quantitative fraction $S_A/\bar{n}$ that the paper argues is large enough to be observable.

What would settle it

Measure the second-order intensity correlation between two concurrently operating gravitational wave detectors: the fixed-number entangled model predicts an excess $g^{(2)} > 1$, whereas a coherent product state gives $g^{(2)} = 1$; observing no excess would rule out the assumed state and collapse the entropy estimate.

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Extended reading notes

Core claim

The paper claims that for two detectors operating concurrently with overlapping graviton state functions, the measurement-induced entanglement entropy of either detector is not negligibly small. Modeling the graviton field as a pure bipartite number state with fixed total $n = 2\bar{n}$ and symmetric Gaussian Schmidt coefficients of variance $\sigma^2 = \bar{n}$, the reduced density matrix of subsystem $A$ yields an entanglement entropy whose large-$\bar{n}$ asymptote is $S_A \sim \tfrac{1}{2}\ln(2\pi e \bar{n})$ (Eq. 17). Normalized by the mean detector graviton number, this gives $S_A/\bar{n}$ on the order of a few percent in the sensitivity range of contemporary detectors, rising as the strain amplitude decreases. The authors take this to mean the bipartite entanglement produced during detection should be discernible from noise with appropriate measurement schemes, even though the same detectors are far too inefficient to projectively detect individual gravitons.

Load-bearing premise

The load-bearing premise is that the two-detector graviton state is a pure state with fixed total number and Gaussian Schmidt coefficients; if the field is instead in the coherent state expected from a classical source, the bipartite state is a product state and the entanglement entropy is exactly zero.

Editorial extensions

If this is right

  • Two existing gravitational wave detectors running coincidentally could show excess coincidence rates of order a few percent above the classical expectation, without any single-graviton projective measurement.
  • As strain sensitivity improves and the detectable strain amplitude $h$ decreases, $\bar{n}$ becomes smaller and the normalized entanglement entropy grows, making the non-classicality signature easier to discern.
  • The proposed signature is tied to the detection process, so it is not suppressed by the extremely low graviton-photon interaction efficiency that limits production-induced entanglement proposals.
  • Extensions to cross- and plus-polarization multimode entanglement would provide complementary signatures for future detectors.
  • If confirmed, the effect would constitute evidence for the quantization of gravity, because a fully classical coherent field would produce no bipartite entanglement.

Reading between the lines

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

  • Editorial extension: the same Gaussian fixed-number entanglement model could be tested in tabletop quantum-optics experiments, where the state can be engineered and the predicted $g^{(2)}$ excess measured directly, before committing gravitational wave observatories to the search.
  • Editorial extension: the entropy estimate is sensitive to the choice of Schmidt coefficient variance; computing $S_A$ for other variance scalings would show whether the log-asymptote is a robust feature of symmetric fixed-number bipartite states or an artifact of setting $\sigma^2 = \bar{n}$.
  • Editorial extension: because a coherent product state gives exactly zero bipartite entropy, this proposal doubles as a sharp falsifiable discriminator between classical and quantized gravitational radiation, and a null coincidence result would undercut the fixed-number assumption rather than merely being noise.
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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. The paper proposes that coincident two-detector gravitational wave observations can exhibit measurement-induced entanglement entropy, offering a signature of graviton non-classicality that avoids the difficulty of single-graviton projective detection. The authors construct a pure bipartite state with fixed total graviton number n, assume Gaussian occupation amplitudes with variance sigma^2 = nbar (Eq. 10), compute the reduced density matrix and entanglement entropy (Eqs. 7 and 11), and derive the asymptotic S_A ~ 1/2 ln(2*pi*e*nbar) (Eq. 17). They conclude that the normalized entropy S_A/nbar is on the order of a few percent for realistic strain amplitudes and should be discernible from noise, and they survey possible observational schemes (Section V). The paper also estimates the mean detector graviton number and detector efficiency in Section II.

Significance. If the central claim were supported by a concrete physical model, this would be a valuable step toward quantum-gravity signatures that do not require single-graviton detection. The entropy calculation itself is transparent, and the asymptotic analysis leading to Eq. (17) is a correct mathematical exercise for the stated Gaussian ansatz. However, the physical input is asserted rather than derived: no measurement operator, interaction Hamiltonian, or postselection mechanism produces Eq. (10), and the claimed detectability is not tied to any noise or signal-to-noise calculation. The result therefore currently has the status of an illustrative calculation for a particular un-justified ansatz rather than a prediction for gravitational wave detectors.

major comments (3)
  1. [Section IV, Eq. (10)] The Gaussian amplitude ansatz c(n,k) = N_g exp[-(k-nbar)^2/(4*sigma^2)] with sigma^2 = nbar is introduced by assertion ("assume Gaussian amplitudes"), not derived from a measurement operator, POVM, conditional postselection, or interaction Hamiltonian. The central quantitative result depends directly on this choice: for Gaussian Schmidt weights with variance a*nbar, the entropy would scale as S_A ~ 1/2 ln(2*pi*e*a*nbar), so the "few percent" value is a property of the chosen a=1. A concrete detection model that produces Eq. (10) is necessary to support the claim that this is the entanglement entropy of a gravitational wave detection.
  2. [Section III] The paper does not explain why a gravitational wave, which for classical astrophysical sources is standardly described by a coherent state, would acquire a fixed-total-number Gaussian Schmidt spectrum during measurement. A coherent state under a bipartite detector split is a product state, giving S_A = 0. The text never addresses this tension or specifies the mechanism by which detection induces the number-projected entangled state. Without such a mechanism, the central claim is unsupported.
  3. [Section V] The statement that the entanglement should be discernible from the noise is not backed by any signal-to-noise, variance, or coincidence-rate calculation. Table I lists candidate schemata (HBT interferometry, squeezed-state measurements, residual noise, atom interferometry), but none is connected quantitatively to S_A/nbar. A quantitative link between the computed entropy and an observable, including the relevant noise floor, is required before the detectability conclusion can be accepted.
minor comments (6)
  1. [Section I] In the Introduction, "non-classically" should be "non-classicality" (paragraph 1).
  2. [Section II] In the sentence following Eq. (2), "justifying the our use" is a typo and should read "justifying our use".
  3. [Section II] The text says "exceeding low detector efficiencies" in the last paragraph; this should be "exceedingly low".
  4. [Fig. 2] The horizontal axis label is unclear: "0 0.5 1 1.5 10^-22" likely denotes strain h in units of 10^-22, but the axis should be labeled explicitly, and the vertical axis needs a label such as S_A/nbar.
  5. [Section VI] The phrase "could provided a better understanding" in the final paragraph of the Discussion should be "could provide a better understanding".
  6. [References] Reference [46] appears garbled: "Class. Quantum Grav.445, 402 (2007)" mixes journal, volume, and page information with what seems to be a duplicate of reference [39]; please correct.

Circularity Check

1 steps flagged · score 6.0 of 10

The few-percent entropy prediction is baked into the Gaussian Schmidt ansatz in Eq. (10), not derived from the detection process.

  1. self definitional [Section IV, Eqs. (10)-(11) and (17); Section VII conclusions]
    "To construct a probability distribution that is symmetric for systems A and B assume Gaussian amplitudes in (3), c (n, k) = N_g (n, ¯n) e^{− (k− ¯n)^2/(4σ^2)} e^{iφ_k} ... where we take σ^2 = ¯n consistent with the Poisson states (9) for large ¯n. ... The asymptote ... S_A ∼ 1/2 ln(2πem)."

    The advertised result, that normalized measurement-induced entanglement entropy is 'on the order of up to a few percent', is obtained by dividing Eq. (17) by ¯n. But Eq. (17) is the entropy of a Gaussian Schmidt spectrum whose variance is set by fiat in Eq. (11) to σ^2 = ¯n. Thus the magnitude of the 'prediction' is an analytic consequence of the chosen state, not a consequence of any measurement model: no operator, POVM, conditional postselection, or decoherence mechanism is specified that would produce λ_g(k) in coincident detections. The coherent-state starting point in Eqs. (8)-(9) is modified ad hoc ('taking α^k → ¯n^{k/2} e^{iφ_k}') and then symmetrized; an actual coherent bipartite field would be a product state with zero entanglement.

full rationale

Internally, the Riemann-sum estimates leading to Eq. (17) are correct and self-contained, and no fitted data or restrictive uniqueness theorem is used. The circularity is narrower: the physical claim of a few-percent normalized entropy is essentially the logarithm of the assumed Schmidt variance divided by that variance. Eq. (11) sets σ^2 = ¯n by fiat, Eq. (17) returns S_A ∼ 1/2 ln(2πe¯n), and dividing by ¯n gives the few-percent number quoted in the abstract, Section V, and conclusions. No detection operator or postselection is shown to produce the symmetric Gaussian Schmidt coefficients; the coherent-state reference would instead give a product state, and the replacement α^k → ¯n^{k/2} e^{iφ_k} is ad hoc. Thus the central quantitative result reduces to the ansatz, with independent content limited to the mathematical evaluation of that ansatz. The self-citations (e.g., [13]) concern detector-response estimates and are not load-bearing for the entropy calculation. Score 6 reflects partial circularity: the derivation is internally valid, but the headline 'prediction' is imposed by the state choice rather than derived from detector physics.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The ledger shows that the central result rests on a small number of ad hoc modeling choices: the fixed-number Gaussian state and the identification of its variance with the mean graviton number. These are not derived from a measurement theory, so the calculation is a self-contained exercise rather than a prediction from established physics.

free parameters (1)
  • Gaussian variance sigma^2 = sigma^2 = n-bar
    The variance of the Gaussian occupation amplitudes in Eq. (11) is chosen equal to the mean detector graviton number, without independent justification; it directly controls the entropy magnitude.
assumptions (3)
  • ad hoc to paper The bipartite detector state is a pure state with fixed total number n = 2 n-bar.
    The fixed-number assumption is introduced in Section III without a derivation from a measurement process on the gravitational field.
  • domain assumption The detector response is treated classically while the signal is quantized.
    Semi-classical approximation stated in Section II.
  • domain assumption Entanglement entropy of a pure bipartite state is a valid signature of non-classicality.
    Implicit throughout the paper; no justification is given for why this measure is appropriate for gravitational wave detection.

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Cite this review

Pith. "Pith review of Measurement-induced entanglement entropy of gravitational wave detections." pith.science (2026). https://pith.science/paper/L4VFQNNW

@misc{pith2026241115632,
  author       = {Pith},
  title        = {Pith review of: Measurement-induced entanglement entropy of gravitational wave detections},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L4VFQNNW}},
  note         = {Machine review of arXiv:2411.15632}
}
read the original abstract

Research on the projective measurement of gravitons increasingly supports Dysons conclusions that the detection of single gravitons is not physically possible. It is therefore prudent to consider alternative signatures of non-classicality in gravitational wave detections to determine if gravity is quantized. Coincident multiple detector operations make it possible to consider the bipartite measurement-induced entanglement, in the detection process, as a signature of non-classicality. By developing a model of measurement-induced entanglement, based on a fixed number of gravitons for the bipartite system, we demonstrate that the entanglement entropy is on the order of a few percent of the mean number of gravitons interacting with the detectors. The bipartite measurement-induced entanglement is part of the detection process, which avoids the challenges associated with developing signatures of production-induced entanglement, due to the extremely low gravitational wave detector efficiencies. The calculation of normalized measurement-induced entanglement entropy demonstrates the potential of developing physically meaningful signatures of non-classicality based on bipartite detections of gravitational radiation. This result is in stark contrast to the discouraging calculations based on single-point detections.

Figures

Figures reproduced from arXiv: 2411.15632 by the authors.

Figure 1
Figure 1. FIG. 1: Measurement-induced entanglement requires overlap of the graviton state functions [23], over the separation distance [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The measurement-induced entanglement entropy, [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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