{"id":"8983495c-4b98-42ec-8ae7-1a9b028672de","arxiv_id":"2411.15632","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"The authors compute a model-dependent measurement-induced entanglement entropy for bipartite gravitational wave detections and find it can be a few percent of the mean detector graviton number.","lead":"This paper proposes that the entanglement entropy between two coincident gravitational wave detectors could reveal whether gravity is quantized. The authors calculate that this entropy is a few percent of the mean number of gravitons interacting with the detectors.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The few-percent entropy prediction is an artifact of the un-derived Gaussian ansatz in Eq. (10): no measurement model produces it, and a coherent-state gravitational wave has zero bipartite entanglement, so the central claim is unsupported.","rationale":"The paper's central claim is that bipartite gravitational wave detections exhibit a measurement-induced entanglement entropy on the order of a few percent of the mean graviton number, discernible from noise. The entire quantitative result follows from Eq. (10), a fixed-total-number Gaussian Schmidt state chosen for symmetry rather than derived from any measurement protocol. The reader's weakest-assumption analysis identifies exactly this gap, and my stress-test agrees. I verified that the mathematical steps from Eq. (10) to Eq. (17) are coherent, so the issue is not internal arithmetic but physical relevance: the state is the load-bearing assumption. The standard quantum state of a gravitational wave from a classical source is a coherent state, and a coherent state split between two detectors remains a product state with zero entanglement entropy. The paper offers no mechanism by which the detection process transforms this into a Gaussian fixed-number state; it merely calls the process 'measurement-induced' and writes down the state. Because the few-percent signature is not a consequence of any stated measurement operator, it cannot support the conclusion that graviton non-classicality is observable. The additional claim of discernibility from noise is also unsupported by any signal-to-noise calculation, but it is downstream of the state-ansatz problem. A concrete derivation from an explicit measurement model, or even the minimal coherent-state postselection check, would settle whether the prediction survives contact with detector physics. Without that, rejection is appropriate.","tokens_in":9048,"tokens_out":11141,"duration_ms":116513,"concrete_test":"Derive the post-measurement bipartite graviton state from a concrete model of two concurrent detectors: take the standard coherent state |alpha> with mean nbar for the incident GW, apply a specific two-detector detection POVM, and compute the unconditional entanglement entropy of the resulting state. If the result is zero or differs materially from Eq. (17), the few-percent signature is an artifact of Eq. (10). A minimal analytical version of this check is to project |alpha>_A |alpha>_B onto fixed total n = 2 nbar, which gives binomial Schmidt coefficients rather than the Gaussian coefficients of Eq. (10), and recompute S_A/nbar from Eq. (7); this tests whether the assumed width sigma^2 = nbar is what an actual coherent-state postselection produces.","verdict_should_be":"REJECT","load_bearing_attack":"The entropy calculation in Section IV is internally correct: for the fixed-number state (10) with Gaussian amplitudes and sigma^2 = nbar, Eq. (7) gives S_A ~ 1/2 ln(2*pi*e*nbar), Eq. (17). But that state is introduced by assertion ('assume Gaussian amplitudes'), not obtained from the measurement process the paper invokes. No operator, POVM, conditional postselection, or decoherence mechanism is specified that would produce lambda_g(k) in actual concurrent GW detections. A gravitational wave from a classical source is a coherent state, whose two-mode decomposition is a product state; the reduced state is pure and S_A = 0. The paper never explains why detection induces a fixed-total-number Gaussian Schmidt spectrum rather than preserving the coherent-state product structure. Consequently 'on the order of a few percent' and 'should be discernible from the noise' are properties of the chosen ansatz, not predictions derived from detector physics. Section V lists possible experimental schemata but contains no noise or signal-to-noise calculation connecting S_A/nbar to an observable; this is an additional unsupported step. The central claim requires either a derivation of Eq. (10) from a concrete measurement model or a demonstration that the result is robust across physically motivated states.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":9319,"tokens_out":7665,"duration_ms":71862,"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":[{"comment":"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.","section":"Section IV, Eq. (10)"},{"comment":"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.","section":"Section III"},{"comment":"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.","section":"Section V"}],"minor_comments":[{"comment":"In the Introduction, \"non-classically\" should be \"non-classicality\" (paragraph 1).","section":"Section I"},{"comment":"In the sentence following Eq. (2), \"justifying the our use\" is a typo and should read \"justifying our use\".","section":"Section II"},{"comment":"The text says \"exceeding low detector efficiencies\" in the last paragraph; this should be \"exceedingly low\".","section":"Section II"},{"comment":"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.","section":"Fig. 2"},{"comment":"The phrase \"could provided a better understanding\" in the final paragraph of the Discussion should be \"could provide a better understanding\".","section":"Section VI"},{"comment":"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.","section":"References"}],"recommendation":"reject","confidential_remarks":"The manuscript addresses an interesting question and the entropy calculation is internally consistent, but the physical basis for the central state ansatz is missing. In my view, the required derivation of Eq. (10) from a measurement process is not a local fix but the core missing element of the paper; without it, the \"few percent\" prediction and the detectability claim do not follow. I would encourage the authors to either derive the fixed-total-number Gaussian state from a concrete detector model or demonstrate that the result is robust across physically motivated states, and to add a quantitative noise analysis connecting S_A/nbar to an observable. The paper may then be suitable for resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the entropy calculation is correct; the physical step isn't. The paper derives S_A ∼ 1/2 ln(2πen̄) for a fixed-total-number bipartite state with Gaussian Schmidt weights of variance n̄, and the asymptotics in Eqs. (13)–(16) are sound. But that state is introduced by assertion in Eq. (10), not derived from any measurement process. No POVM, conditional postselection, or decoherence mechanism is given that would produce those amplitudes in a real gravitational wave detection. For a classical source the natural state is a coherent state, whose two-mode decomposition is a product; the reduced state is pure and the entanglement entropy is zero. The paper never explains why detection should convert a coherent state into an entangled fixed-number Gaussian state. So the 'few percent' and 'discernible from the noise' claims are properties of the ansatz, not predictions about detectors.\n\nWhat is genuinely new: applying measurement-induced entanglement of identical particles to concurrent gravitational wave detectors, as an alternative to single-graviton detection and production-induced entanglement. That framing is worth taking seriously, and the paper is honest about the difficulty of measuring entropy (Section V admits it) before listing possible schemata. Credit where due: the mathematics from Eq. (7) to (17) is correct, and the Riemann-sum estimates are properly handled.\n\nSoft spots: Section V is a menu, not a protocol. There is no noise model, no signal-to-noise estimate, and no argument that increased coincidence rates would be observable. Table I lists HBT, squeezed states, and atom interferometry without quantitative connection to S_A. The claim that Poisson amplitudes are 'unphysical' is asserted; even if that's right, it doesn't justify choosing a different ansatz unless the ansatz comes from the detection process. A more serious problem is that the calculation assumes a pure fixed-number state; gravitational wave detectors operate on states with uncertain photon/graviton number and significant environment coupling. The robustness of the result to these realities is not examined.\n\nWho is this for? People thinking about quantum-gravity phenomenology and the Dyson single-graviton argument. It's a speculative theory paper with a central unsupported step. I would not cite it in my own work, but I'd bring it to a reading group: it's a good case study in the difference between a calculation and a prediction. If it comes across my desk, I'd send it to a referee rather than desk reject it: the referee report is short and the question is live. But I'd expect rejection unless the authors derive Eq. (10) from a concrete measurement model.","headline":"A correct entropy calculation for an arbitrary Gaussian ansatz; the few-percent 'signature' is not derived from detector physics.","tokens_in":9792,"tokens_out":3911,"would_cite":false,"duration_ms":34475,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.30.Nk","04.30.Tv","04.40.Dg","04.62.+v","11.15.Kc","95.55.Ym"],"model":"deepseek-v4-flash","headline":"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.","keywords":["gravitational waves","graviton","entanglement entropy","measurement-induced entanglement","bipartite detection","non-classicality","intensity-correlation interferometry","quantum gravity"],"falsifier":"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.","tokens_in":8857,"feed_emoji":"🌊","tokens_out":14284,"duration_ms":117651,"temperature":0.7,"pith_summary":"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.","feed_headline":"Gravitational wave detectors could reveal graviton entanglement","feed_subtitle":"A few-percent entropy signal could make quantum gravity visible to existing detectors.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Establishes the premise that single-graviton projective detection is physically impossible, motivating an alternative non-classicality signature.","marker":"[1]"},{"why":"Supplies the semi-classical detector response energy used to estimate the mean interacting graviton number in Eq. (1).","marker":"[3]"},{"why":"Supplies the graviton creation and annihilation operator number-state formalism, simplifying the model to a single polarization.","marker":"[12]"},{"why":"Supplies the gravito-optics framework, detector energy and flux estimates, and the intensity-correlation detection scheme.","marker":"[13]"},{"why":"Provides the model of measurement-induced entanglement for identical particles on which the bipartite detector state is built.","marker":"[18]"},{"why":"Supplies the later measurement-induced entanglement formalism that grounds the fixed-number bipartite construction.","marker":"[20]"},{"why":"Defines the requirement of overlapping state functions for identical-particle entanglement, which selects the detector geometry.","marker":"[23]"},{"why":"Provides the bipartite number-state formalism and the coherent-state amplitude pattern that motivates the Gaussian Schmidt coefficients.","marker":"[33]"}],"fun_headline_variants":["Graviton entanglement entropy measurable in twin detectors","Bipartite detection reveals few-percent graviton entanglement","Twin detectors capture graviton entanglement entropy","Graviton entanglement may surface in detector pair entropy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Graviton entanglement entropy measurable in twin detectors","Bipartite detection reveals few-percent graviton entanglement","Twin detectors capture graviton entanglement entropy","Graviton entanglement may surface in detector pair entropy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000308,"raw_usage":{"total_tokens":1747,"prompt_tokens":921,"completion_tokens":826,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":537,"completion_tokens_details":{"reasoning_tokens":765}},"tokens_in":537,"tokens_out":826,"duration_ms":7282,"temperature":1.0,"reasoning_tokens":765,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:05:21.351488+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the premise that single-graviton projective detection is physically impossible, motivating an alternative non-classicality signature."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the semi-classical detector response energy used to estimate the mean interacting graviton number in Eq. (1)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the gravito-optics framework, detector energy and flux estimates, and the intensity-correlation detection scheme."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the model of measurement-induced entanglement for identical particles on which the bipartite detector state is built."},{"cited_title":"Schroeder, Am","cited_arxiv_id":null,"evidence_quote":"Supplies the later measurement-induced entanglement formalism that grounds the fixed-number bipartite construction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the bipartite number-state formalism and the coherent-state amplitude pattern that motivates the Gaussian Schmidt coefficients."}],"review_version":1}