{"id":"b4fe07a0-f7e1-4dce-a82d-1a4d711ce4a4","arxiv_id":"2608.00907","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"For current experimental parameters, SU(1,1) interferometers give no Fisher-information advantage over SU(2) for spacetime fluctuation estimation; with assumed future low-loss, high-power parameters they do.","lead":"This paper calculates how precisely two types of laser interferometers could measure random spacetime fluctuations, and compares a standard interferometer with a more exotic one. It finds that with today's technology the exotic version offers no advantage, but with assumed future improvements it could.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper applies the Gaussian-state QFI formula (Eq. 24) to the ensemble-averaged output state, but the average of phase-rotated Gaussian states is non-Gaussian; non-Gaussian corrections enter at the same order in Γ, so the reported QFI values and advantage ratios are not established.","rationale":"After reading the full text, the strongest candidate for a load-bearing flaw is indeed the one identified by the reader: the paper's own statement in Sec. III, 'As the states of interest are Gaussian,' is where the argument is most fragile. The states are Gaussian before the ensemble average; the average over spacetime fluctuations turns them into a mixture. The paper computes the displacement and covariance of the mixture and then feeds these into the Gaussian QFI formula. A simple perturbation calculation for a coherent state with Gaussian phase noise shows that the exact QFI has a 1/Γ term with coefficient given by the variance of the phase generator, while the Gaussian-state formula using the same first and second moments gives half that coefficient. This means the non-Gaussianity is not a higher-order correction; it changes the leading-order QFI. Since the central claim is a quantitative comparison of Fisher informations (Eqs. 29–35 and Table I), the numbers are not reliable without either deriving the exact QFI of the phase-averaged state or proving that the non-Gaussian corrections cancel in both interferometers. The paper honestly caveats the current-experiment no-advantage result and the low-squeezing limit, but that does not repair the technical gap. I therefore see no reason to change the reader's REJECT verdict. The proposed perturbation test would settle the matter: if the exact leading coefficient coincides with Eq. (24) for both interferometers, the concern would be resolved; if not, the comparison must be redone.","tokens_in":12642,"tokens_out":45136,"duration_ms":517079,"concrete_test":"Using the setup of Sec. III, expand the exact phase-averaged output state as ρ(Γ) = ρ0 + ΓL + O(Γ²) for the lossless SU(2) and SU(1,1) interferometers, with L = ρ'(0). Compute the exact leading QFI coefficient Q_Γ ≈ Tr(Π L Π)/Γ, where Π = 1 - ρ0, and compare it with the prediction of Eq. (24) for the same L. Do this at β = 0 and at β = 10 dB, both with and without loss. As a simpler diagnostic, evaluate the single-mode coherent-state test case: exact Q_Γ = α²σ/Γ versus Eq. (24)'s α²σ/(2Γ) + O(Γ⁰). If the coefficients differ for either interferometer, Eq. (29) and Table I are incorrect at leading order; if they agree, the Gaussian-state assumption would be vindicated at the relevant order.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Sec. II, D and C are obtained by averaging the output state over the Gaussian spacetime fluctuations (Eqs. 2–3), and Sec. III then applies the Gaussian-state QFI formula (Eq. 24) from Monras. This is the load-bearing step: for each fixed realization of Φc, Φd the output is Gaussian, but the ensemble average is a mixture of rotated Gaussian states, which is not Gaussian. The paper does not show that the non-Gaussian part of the phase-averaged state is negligible at the order retained. A direct perturbation calculation illustrates the issue: for a single-mode coherent state with phase variance ε = Γσ, the exact QFI for Γ has a leading term Tr(Π L Π)/Γ, where L = ρ'(0) = -1/2[N,[N,ρ0]]; for a coherent state this coefficient is α²σ. Applying Eq. (24) to the Gaussian state with the same mean and covariance gives a coefficient α²σ/2 (from the covariance term) plus a subleading α²σ². Thus the Gaussian-state formula underestimates the leading QFI by a factor of two in this simple case, and the discrepancy is of the same order in Γ, not a higher-order correction. Since Eqs. (29), (30), (32) and Table I all rest on Eq. (24), the central comparison between SU(1,1) and SU(2) interferometers is not established without a computation using the true phase-averaged state or a proof that the non-Gaussian contributions cancel in both interferometers.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper compares the quantum Fisher information (QFI) for estimating the strength Γ and correlation length ℓ of random spacetime phase fluctuations in an SU(2) Mach–Zehnder interferometer and an SU(1,1) interferometer with two OPAs. For Gaussian input states and a stationary Gaussian model of the fluctuations, the author computes the output displacement vector and covariance matrix in the presence of loss, then applies the Gaussian-state QFI formula (Eq. (24)) and corresponding classical Fisher information for homodyne and photon-counting measurements. The central findings are that, under current experimental parameters, the SU(1,1) interferometer offers no advantage over the SU(2) interferometer, whereas under assumed future parameters (α = 10^10, η = 5×10^-6) it offers a QFI/CFI advantage with ratios between 1.8 and 6.3 (Table I). The paper also derives a saturation condition e^{-2β} << (1−η)σ̃ for reaching the maximum scaled QFI of 1/2.","tokens_in":13043,"tokens_out":8190,"duration_ms":102999,"significance":"If the results were correct, they would provide useful quantitative guidance for ongoing and proposed interferometric searches for spacetime fluctuations, in particular identifying the parameter regimes in which SU(1,1) interferometry could be competitive. The paper is transparent about the hypothetical nature of the future-advantage parameters and about the fact that current parameters yield no advantage; this is a genuine strength. However, the central calculation rests on an unjustified application of the Gaussian QFI formula to a non-Gaussian phase-averaged state; the reported values and advantage ratios are therefore not established. The manuscript is clearly written and cites relevant experimental programs, but the main quantitative claim is not supported by the derivation as presented.","major_comments":[{"comment":"The output state after averaging over the random phases Φ_c, Φ_d is a convex mixture of Gaussian states, not a Gaussian state. Equations (13)–(17) determine only the first and second moments of that mixture. The QFI formula (24) from [30] applies only to Gaussian states, and the QFI of a Gaussian with the same moments is not generally equal to the QFI of the mixture. The discrepancy is not a higher-order correction: for a single-mode coherent state with a random phase of variance ε = Γσ, the exact QFI for Γ has leading coefficient α²σ, whereas applying Eq. (24) to the Gaussian with the same mean and covariance gives α²σ/2. Since Eqs. (29), (30), (32), (35), and Table I are all derived from Eq. (24), the reported QFI values and the SU(1,1)-vs-SU(2) comparison are not established by the manuscript as written.","section":"Section III, Eq. (24); Section II, Eqs. (13)–(17)"},{"comment":"The photon-number CFI is computed from the Wigner function W(Z) in Eq. (27) of a Gaussian state with averaged covariance. For the actual ensemble, W(Z) is the average of the individual Gaussian Wigner functions over Φ_c, Φ_d; this ensemble Wigner function is not of the Gaussian form (27). Hence the p_j used in Eq. (26) are not the true photon-number probabilities for the phase-averaged state, and the statement that photon counting at the dark port is optimal (after Eq. (31)) is likewise unsupported. This is the same underlying issue as the first comment, but it invalidates the CFI results independently of the QFI formula.","section":"Section III, Eqs. (26)–(28)"}],"minor_comments":[{"comment":"The text says C_ii is the variance of the Gaussian probability distribution, but with the quadrature normalization in Eq. (5) the variance is C_ii/2. The formula is consistent with treating C_ii as twice the variance; the wording should be adjusted to avoid confusion.","section":"Section III, Eq. (25)"},{"comment":"There are several typos: 'dispacement' (Eq. 21 caption), 'dispalcement' (line after Eq. 21), 'dicrete' (Section III), 'experimenets' (Section III), 'undepeleted' (Section III), 'possiblilty' (Introduction), 'interfeometer' (Appendix A). A careful proofread is needed.","section":"Throughout"},{"comment":"The definitions of σ and ξ should state explicitly that they are dimensionless and should define the domain of ρ consistently; the current alignment and notation make the correlation integrals hard to parse.","section":"Eqs. (4a)–(4b)"},{"comment":"The vectorisation convention for ⃗C is not stated. Please define how the 4×4 covariance matrix is vectorised so that the expression (C ⊗ C − M ⊗ M)^{-1} is unambiguous.","section":"Eq. (24)"},{"comment":"The description of n as 'the maximum number of photons up to which the photons are being counted discretely' is unclear. Please specify how n is chosen, how Q is evaluated, and whether the results in Fig. 2 depend strongly on the truncation n.","section":"Section III, Eq. (26)"}],"recommendation":"reject","confidential_remarks":"The central issue is not a missing proof that could be supplied in a minor revision; the perturbation example shows an order-one error at leading order in the fluctuation strength. A simple revision within the current covariance-matrix framework would not fix the problem, because the true QFI requires information beyond the first and second moments of the phase-averaged state. The manuscript is clearly written and the author is appropriately cautious about current vs future parameters, but the main quantitative claim is not established. I would encourage the author to undertake a calculation of the QFI for the actual phase-averaged (non-Gaussian) state; if that calculation confirms the reported advantage ratios, the work could be resubmitted as a new paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nHere's my take on arXiv:2608.00907. The headline is: the central comparison rests on a Gaussian assumption that the paper does not justify, and the numbers are probably wrong. The paper computes quantum Fisher information for estimating the strength and correlation length of spacetime fluctuations in SU(2) and SU(1,1) interferometers, with loss, and gives ratios of ~1.8–6.3 for optimistic future parameters. That's a useful question, and the author is properly honest: for currently realistic SU(1,1) parameters there's no advantage, and they flag the low-squeezing caveat. The comparison of CFI for homodyne and photon-counting is also new as far as I know.\n\nThe problem: after averaging over the stochastic phases Φc, Φd, the output state is a mixture of infinitely many Gaussian states. A mixture of Gaussian states with different displacement phases is not Gaussian. The paper nevertheless applies Monras's Gaussian QFI formula, Eq. (24), to the averaged covariance matrix and displacement. That step is incorrect unless the non-Gaussian character can be shown to be negligible. The stress-test gives a simple single-mode example where the Gaussian formula underestimates the leading-order QFI by a factor of two, and the discrepancy is at the same order in Γ. So the numbers in Eqs. (29)–(35) and Table I are not established. The same suspicion applies to the CFI expressions, which use Gaussian probability densities derived from the averaged covariance matrix.\n\nMinor points: the model for spacetime fluctuations is borrowed from the author's own Ref. [31]; that's fine, it's not fitting. The paper contains no machine-checked proof or numerical code, so we have no independent check.\n\nWho is this for? People designing table-top interferometer searches for quantum-gravity signals. The qualitative conclusion – current SU(1,1) isn't competitive, future low-loss ones might be – could still be right, but I wouldn't bet on it based on this calculation.\n\nMy recommendation: send it to a serious referee. The question is worth asking, and the error is technical and might be fixable with a proper treatment of the phase-averaged state. But as it stands I would not rely on any of the quantitative results.","headline":"Central QFI numbers rest on a Gaussian-state formula applied to a non-Gaussian averaged state; the advantage ratios are not established.","tokens_in":13504,"tokens_out":2842,"would_cite":false,"duration_ms":30841,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Currently achievable SU(1,1) interferometers give no advantage over SU(2) interferometers for estimating the strength or correlation length of spacetime fluctuations; the advantage appears only for assumed future parameters with higher ligh","keywords":["quantum Fisher information","SU(1,1) interferometry","SU(2) interferometry","spacetime fluctuations","stochastic phase estimation","Gaussian states","squeezing","optical loss"],"falsifier":"Numerically compute the exact quantum Fisher information of the ensemble-averaged output state—a continuous mixture of phase-rotated Gaussian states—without invoking Eq. (24), for the same parameters as Fig. 2(b). If the exact QFI disagrees with Eq. (29) or with the Table I ratios, the central comparison collapses; a laboratory check could compare the measured Wigner function of the output with the Gaussian covariance-matrix prediction.","tokens_in":1950,"feed_emoji":"⚛️","tokens_out":3689,"duration_ms":110176,"temperature":0.7,"pith_summary":"This paper asks whether replacing the beamsplitter in a laser interferometer with optical parametric amplifiers—the SU(1,1) design—improves our ability to estimate the strength and correlation length of random spacetime fluctuations. By computing quantum and classical Fisher information for Gaussian states, with and without internal loss, the author finds that at current experimental parameters the SU(1,1) interferometer provides no advantage over the conventional SU(2) interferometer. The advantage appears only in an assumed future regime with much higher input light intensity and much lower loss, where the quantum Fisher information ratio reaches roughly 1.8 to 6.3. The calculation also shows that both interferometers reach the same universal information ceiling, so the practical winner is determined by loss and by which measurement is convenient.","feed_headline":"SU(1,1) interferometers offer no current edge in spacetime-noise sensing","feed_subtitle":"Active-squeezing design only wins with brighter light and far lower loss.","key_machinery":"The load-bearing object is the Gaussian-state quantum Fisher information formula, Eq. (24), which reduces QFI to derivatives of the displacement vector and the covariance matrix. The paper feeds into it the ensemble-averaged covariance matrices $C^{(2)}$ (Eq. 14) and $C^{(11)}$ (Eq. 17), computed to leading order in the fluctuation strength $\\Gamma$, and derives the closed-form scaled QFI Eq. (29), whose two branches set the universal ceiling $1/2$ and the loss-limited value $(1-\\eta)\\tilde{\\sigma}$. This identity is what turns the comparison into a question of experimental parameters rather than of interferometer topology.","core_discovery":"The central claim is that for estimating the variance (strength) and correlation length of a stationary Gaussian spacetime-fluctuation signal, the quantum Fisher information is identical in form for SU(2) and SU(1,1) interferometers: $Q_s=(1-\\eta)\\tilde{\\sigma}$ in the low-squeezing limit and $Q_s=1/2$ once $e^{-2\\beta}\\ll(1-\\eta)\\tilde{\\sigma}$. The difference is entirely in the attainable parameters: conventional interferometers operate near lossless with bright coherent light, while current SU(1,1) interferometers are lossy and intensity-limited, which erases their formal advantage. With hypothetical future parameters ($\\alpha=10^{10}$, $\\eta=5\\times10^{-6}$), the SU(1,1) interferometer's","pith_inferences":["If the Gaussian-mixture approximation holds, the two-branch QFI formula suggests the practical ranking of interferometers is set by loss and input intensity, not by SU(2) versus SU(1,1) topology; a resource comparison that includes measurement time and the need for high-$n$ photon counting could weaken the future-advantage ratios.","One extension: compute the full $2\\times2$ Fisher information matrix for joint estimation of $(\\Gamma,\\ell)$, since the equality of the single-parameter scaled QFIs does not guarantee that the two parameters are independently estimable.","A direct numerical check of the exact QFI for the phase-rotated Gaussian mixture, outside the Gaussian-state formula, would be a decisive test of the Table I ratios; the paper does not perform this check.","The universal saturation at $Q_s=1/2$ suggests that once the squeezing condition is met, further squeezing adds no information for this noise model; this could serve as a design target for detector optimization."],"forward_implications":["For both interferometers, the scaled QFI for estimating the fluctuation strength $\\Gamma$ takes the closed form $Q_s=(1-\\eta)\\tilde{\\sigma}$ at low squeezing and saturates at $1/2$ once $e^{-2\\beta}\\ll(1-\\eta)\\tilde{\\sigma}$.","The same two-branch formula holds for estimating the correlation length $\\ell$, so conclusions about advantage carry over unchanged from $\\Gamma$ to $\\ell$.","At currently achievable parameters ($\\alpha=10^{10}$, $\\eta=5\\times10^{-6}$ for SU(2); $\\alpha=10^4$, $\\eta=0.4$ for SU(1,1)), the SU(1,1) interferometer never beats the SU(2) interferometer in the metrics considered.","If future SU(1,1) interferometers match SU(2) brightness and loss ($\\alpha=10^{10}$, $\\eta=5\\times10^{-6}$), the Fisher-information ratios are 1.79–1.93 at 6 dB and 4.28–6.33 at 10 dB squeezing.","Within the SU(2) design, photon counting at the dark port with $n=1$ is optimal and reaches half the QFI, whereas the SU(1,1) design lacks such a convenient optimal measurement."],"supporting_citations":[{"why":"Supplies the phase-space formula for quantum Fisher information of Gaussian states (Eq. 24), the central tool for all QFI computations.","marker":"[30]"},{"why":"Defines the stochastic-phase estimation problem and gives the baseline whose lossless QFI the SU(2) result is compared with.","marker":"[19]"},{"why":"Motivates the question by claiming SU(1,1) interferometers surpass conventional ones for estimating a fluctuating phase variance.","marker":"[26]"},{"why":"Provides the spacetime-fluctuation correlation model and the phase-noise definitions entering Eq. (1).","marker":"[31]"},{"why":"Supplies current experimental SU(2) parameters, including low loss and bright coherent input.","marker":"[16]"},{"why":"Supplies the photon-counting interferometry context and parameters used for the conventional interferometer.","marker":"[32]"},{"why":"Supplies the first experimental realization of the SU(1,1) interferometer with parametric amplifiers.","marker":"[22]"},{"why":"Supplies current SU(1,1) parameters, including high parametric gain and intensity limits, used in the comparison.","marker":"[24]"},{"why":"Supplies a recent truncated SU(1,1) interferometer realization and its loss parameters.","marker":"[33]"}],"fun_headline_variants":["SU(1,1) interferometers lose practical edge in spacetime-noise tests","No current gain from SU(1,1) interferometers for spacetime noise","SU(1,1) interferometers: only future tech beats SU(2) for noise sensing","Spacetime noise estimation: SU(1,1) formal gain erased by loss and dim light","SU(1,1) interferometer edge requires bright light and ultra-low loss"],"cache_read_input_tokens":15232,"weakest_assumption_plain":"The entire comparison rests on treating the ensemble-averaged output state as Gaussian, so that the quantum Fisher information is fixed by the mean and covariance; a mixture of Gaussian states rotated by different random phases is generally not Gaussian, and if that approximation fails the reported QFI and CFI numbers are unproven.","fun_headline_variants_meta":{"raw":{"variants":["SU(1,1) interferometers lose practical edge in spacetime-noise tests","No current gain from SU(1,1) interferometers for spacetime noise","SU(1,1) interferometers: only future tech beats SU(2) for noise sensing","Spacetime noise estimation: SU(1,1) formal gain erased by loss and dim light","SU(1,1) interferometer edge requires bright light and ultra-low loss"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000309,"raw_usage":{"total_tokens":1604,"prompt_tokens":751,"completion_tokens":853,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":495,"completion_tokens_details":{"reasoning_tokens":741}},"tokens_in":495,"tokens_out":853,"duration_ms":9547,"temperature":1.0,"reasoning_tokens":741,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T00:41:17.767862+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Numerically compute the exact quantum Fisher information of the ensemble-averaged output state—a continuous mixture of phase-rotated Gaussian states—without invoking Eq. (24), for the same parameters as Fig. 2(b). If the exact QFI disagrees with Eq. (29) or with the Table I ratios, the central comparison collapses; a laboratory check could compare the measured Wigner function of the output with the Gaussian covariance-matrix prediction.","supporting_citations":[{"cited_title":"Patra, L","cited_arxiv_id":null,"evidence_quote":"Supplies the phase-space formula for quantum Fisher information of Gaussian states (Eq. 24), the central tool for all QFI computations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the stochastic-phase estimation problem and gives the baseline whose lossless QFI the SU(2) result is compared with."},{"cited_title":"Amelino-Camelia, Gravity-wave interferometers as quantum-gravity detectors, Nature 398, 216 (1999)","cited_arxiv_id":null,"evidence_quote":"Motivates the question by claiming SU(1,1) interferometers surpass conventional ones for estimating a fluctuating phase variance."},{"cited_title":"Ruo Berchera, I","cited_arxiv_id":null,"evidence_quote":"Provides the spacetime-fluctuation correlation model and the phase-noise definitions entering Eq. (1)."},{"cited_title":"Ruo-Berchera, I","cited_arxiv_id":null,"evidence_quote":"Supplies the photon-counting interferometry context and parameters used for the conventional interferometer."},{"cited_title":"Jarzyna and R","cited_arxiv_id":null,"evidence_quote":"Supplies the first experimental realization of the SU(1,1) interferometer with parametric amplifiers."},{"cited_title":"Pezz´ e and A","cited_arxiv_id":null,"evidence_quote":"Supplies current SU(1,1) parameters, including high parametric gain and intensity limits, used in the comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies a recent truncated SU(1,1) interferometer realization and its loss parameters."}],"review_version":1}