{"id":"43cd5b0b-5b27-4ed6-8f49-b60c5ffe1853","arxiv_id":"2607.21663","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Coherent over-rotation angles are Fisher-null (CRB infinite) in a single fixed-basis histogram at zero angle; adding ⌈log2(n+1)⌉ extra product-Pauli settings restores identifiability, with conditioning, not coverage, setting the sampling cost.","lead":"A small systematic gate error in a quantum computer is invisible to the cheapest readout: the single measurement histogram barely changes, so no amount of data can find it. The paper proves this blindness, then shows that adding only a logarithmic number of fixed measurement settings makes the error visible and recoverable.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim is sound within its stated Z-diagonal canonical-input scope; the least-secure link is the input's vanishing Y-coherence, without which 'absent' becomes 'faint'.","rationale":"The reader's weakest assumption correctly identifies the Z-diagonal input. I agree that this is the least-secure condition: the entire veiling mechanism at η=0 relies on odd-Y expectations vanishing, and the paper's own Appendix F control shows the kernel's coherent weight drops from 0.99 to 0.55 when a Y-coherent input is used. This makes the 'absent' phenomenon a symmetry-boundary statement rather than an input-generic one. However, the theorems are explicitly and repeatedly scoped to the canonical Z-diagonal input (abstract, Section II, Table I, Section VIII), so the assumption is not a hidden internal flaw. The central Fisher-kernel derivation, the logarithmic separating-code construction, and the conditioning floor are internally consistent and cross-checked against exact computation; I found no error in the rank formula, the exchange-basis argument, the Y-signature lower bound, or the block-diagonal conditioning analysis. The practical relevance claim does inherit fragility from the input assumption, but this does not overturn the paper's mathematical claims. The reader's CONDITIONAL verdict is driven primarily by missing code/data and limited hardware evidence, not by a correctness defect; my concern does not move that verdict. Hence UNCHANGED, with the concrete non-Z-diagonal test recommended as a worthwhile boundary check.","tokens_in":32009,"tokens_out":25344,"duration_ms":271235,"concrete_test":"For n=3, complete weight-1/weight-2 family, compute the single-setting Z-histogram Jacobian at η=0 with input ρ_ε = ⊗_i (|0⟩+i ε_i |1⟩)/√(1+ε_i^2) for ε_i ∈ {0, 0.01, 0.05, 0.1}. Record min over S of ‖∂_{η_S} p(x)|_{η=0}‖ and the Fisher information F_{η_S,η_S}(0). If F is nonzero for any ε>0, the 'absent' statement is confined to exactly Z-diagonal inputs; estimate the scaling (∼ε^2 if the first nonzero term is second-order). Also repeat with an unbiased (real-amplitude) mixed diagonal input ρ=(1-ε)|0⟩⟨0|+ε|1⟩⟨1| to separate diagonal mixing from Y-coherence.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The single least-secure link in the central argument is the Z-diagonal (real, odd-Y-vanishing) input assumption, not the Fisher-kernel algebra, which is internally consistent. The 'absent' claim at η=0 is exactly the statement that every coherent column ∂_{η_S}⟨P⟩ contains an odd-Y partner expectation ⟨i X_S P⟩ (Lemma 1) that vanishes for such inputs. The proof of Theorem 2 and the entire exchange-kernel construction (Appendix A, Lemma 1; Appendix F) depend on this. If the input carries any Y-coherence — e.g., a preparation error producing ⟨Y_i⟩≠0 — then ∂_{η_S}⟨Y_i X_j⟩ is proportional to a nonzero odd-Y expectation, so the Fisher column is nonzero and the coherent angle is faint, not absent. The paper's own Appendix F control (a local SH input) drops the kernel's coherent weight from ≥0.99 to 0.55, confirming the sensitivity. The theorems are explicitly scoped to the canonical |0^n⟩ input, so this is not an internal inconsistency; it is the point where the mathematical result is least protected against exactly the modeling assumption that real devices violate. Practical claims about 'calibration driving η to 0' inherit this fragility: preparation errors that produce Y-coherence partially lift the veil.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper asks whether a fixed computational-basis (Z) histogram can identify small coherent over-rotation angles in a commuting weight-1/weight-2 transverse noise model, in the presence of stochastic Pauli flips, on the canonical |0^n> input. It proves that at zero coherent angle every such angle lies in the Fisher-information kernel, so its singular Cramér–Rao bound is infinite and no finite-variance locally unbiased estimator exists (Theorems 1–2). It then constructs a twirl-free product-Pauli separating code of ⌈log2(n+1)⌉ fixed settings that restores identifiability and is minimal for the complete family at η=0 (Theorem 3), and it analyzes finite-sample cost through a conditioning floor c_B = min{(1−2p)^n, √λ2} with an Ω(η^{-2}) sub-coverage divergence (Theorem 4). The paper includes exact density-matrix checks up to n=8, a design-population numerical study, a classical analogue, and a small hardware consistency check on IBM Heron.","tokens_in":32314,"tokens_out":33262,"duration_ms":280554,"significance":"The core contribution is a clean and useful example where a parameter is absent rather than faint from a passive measurement, and where the cure is measurement design rather than model enrichment. The central theorems are supported by explicit proofs in the appendices, the kernel and separating code are constructive, and the numerical checks match exact evolution to machine precision. The distinction between coverage and conditioning, with a closed-form floor, is a valuable conceptual and practical point. The results are, however, restricted to a narrow regime (Z-diagonal/canonical input, commuting weight-1/2 generators, known support), and the paper honestly states this.","major_comments":[{"comment":"Theorem 4 advertises c_B = min{(1−2p)^n, √λ2} as a closed-form conditioning floor for the complete family, but λ2 is never actually defined or evaluated: the text refers only to 'the second eigenvalue of the readout-restricted information,' and the Z^n incidence Gram spectrum is not given. Without an explicit definition (or a formula/bound for λ2), the √λ2 branch of the floor cannot be verified, and the 'closed-form' claim is incomplete. Please define the readout-restricted information and state λ2 for the complete family, and indicate which branch dominates in the uniform-rate case.","section":"§IV, Theorem 4; Appendix E, Lemma 9"},{"comment":"The 'absent, not faint' claim is proved for Z-diagonal real inputs with vanishing odd-Y expectations, a scope the paper states in Table I and Section VIII. However, the title and the abstract's first paragraph present the absence as a property of the coherent fault itself. The paper's own numerical control with a local SH input (Appendix B) drops the kernel coherent weight from ≥0.99 to 0.55, showing that preparation errors producing Y-coherence partially lift the veil. Since the practical conclusion that calibration drives η to 0 inherits this fragility, please add an explicit scope caveat in the abstract and in Section VIII: for inputs carrying Y-coherence the coherent angle is faint rather than absent.","section":"§III/Appendix B; Abstract"}],"minor_comments":[{"comment":"The constant '2 npmin' in the finite-sample bound should read 2^n p_min; as written (e.g., 'N·MSE≥2 npmin σ−2 min') it is inconsistent with the claim that the constant equals 1 at a uniform reference. Ensure exponents are typeset correctly throughout.","section":"Appendix E / §IV"},{"comment":"Section VIII.b says the sub-coverage divergence is 'stated as a divergence without a precise exponent,' but Theorem 4 states the precise rate Ω(η^{-2}). Rephrase to avoid contradiction.","section":"§VI.b / §VIII.b"},{"comment":"'beyond four qubits it clears entirely' should be qualified as 'at generic moderate angles'; at small angles the rank may still be deficient by the local analysis.","section":"Abstract"},{"comment":"The data-availability statement says the code and data 'will be released publicly with the published version'; for review and reproducibility, please provide a repository link or a permanent availability statement.","section":"Data Availability"}],"recommendation":"minor_revision","confidential_remarks":"This is a solid paper; the central mathematical claims are sound within the stated scope. The two issues I raise are (i) an incomplete definition of λ2 in the main floor theorem and (ii) a scoping caveat for the 'absent' claim. Both are fixable without changing the results. The hardware experiment is only a consistency check and should not be over-interpreted. I recommend minor revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is better than the abstract's hype. The core technical result — at η=0, a single fixed-basis histogram has a Fisher kernel that contains every coherent over-rotation, so no finite-variance locally unbiased estimator recovers it, and ⌈log2(n+1)⌉ additional settings fix it — is proved with real lemmas, not asserted. I checked the appendices; the exchange-kernel rank formula and the c_B floor follow. The multi-qubit Walsh-incidence kernel and the conditioning floor are genuinely new. The single-qubit degeneracy is folklore and the log count comes from group testing, but the paper says so, and the multi-qubit combination is original.\n\nWhat it does well: it gives a closed-form kernel for a concrete, useful noise class, proves non-estimability via the extended CRB, constructs a minimal separating code, and shows conditioning, not coverage, sets sample cost. The exact-computation checks to n=8 are reassuring. The scoping is unusually honest: it says exactly where the theorems hold and where they don't.\n\nSoft spots, in proportion. The stress-test note is right: the Z-diagonal input assumption is load-bearing. The 'absent' claim is literally that the odd-Y Pauli expectations vanish. The paper's own Appendix F shows a non-Z-diagonal state drops the kernel's coherent weight from 0.99 to 0.55. So if your preparation has any Y-coherence, the angle is faint, not absent. The theorems are scoped to |0^n⟩, so it's not an internal error, but it's the exact place where real devices break the assumption. The paper does not hide this, but the title's 'absent' overstates robustness.\n\nSecond, the code and data are not yet released. The reader's 'conditional' verdict is right: the derivation is checkable now, but the finite-sample and hardware numbers need the repo. The hardware evidence is five replicates on two prescreened backends; it's a consistency check, and the paper calls it that. Fine.\n\nThird, the nonzero-angle coherent-fraction claims are numerically checked, not proved. That is a minor gap, and the paper labels it 'checked numerically.' Also the conditioning floor is exponentially small in n at fixed p; the paper calls it a fixed-n guarantee. That is correct but limits practical relevance at large n.\n\nOverall: the central claim holds up within the stated scope. The paper deserves a serious referee. I'd send it, ask for code/data, and want a paragraph on how sensitive the 'absent' claim is to Y-coherence. The right reader gets a clean proof of a narrow but real effect.","headline":"The core impossibility and the logarithmic measurement cure are real and well proved for Z-diagonal inputs; the paper is worth refereeing, but the Z-diagonal assumption is load-bearing and the practical reach is narrower than the title suggests.","tokens_in":32796,"tokens_out":2575,"would_cite":true,"duration_ms":26760,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P68","62B10"],"pacs":["03.67.-a"],"model":"deepseek-v4-flash","headline":"Coherent qubit noise is absent, not faint, from a single histogram, and a logarithmic set of extra measurement settings restores it.","keywords":["coherent over-rotation","Fisher information kernel","singular Cramér-Rao bound","measurement design","separating code","conditioning floor","qubit characterization","coherence veil"],"falsifier":"Prepare |0^n⟩ with a single known over-rotation of angle η on one qubit and measure the Z-basis histogram at η=0 and at small η: the claim predicts the histogram's first-order derivative with respect to η is exactly zero at η=0 (the Fisher column vanishes), while a generic nonzero angle gives a small but nonzero slope. Equivalently, prepare the same over-rotation on an input with Y coherence (e.g., |+⟩ rotated by a small phase) and measure a single Z histogram: the paper's mechanism predicts the coherent angle immediately becomes visible from that single histogram, since the odd-Y expectation","tokens_in":31923,"feed_emoji":"⚛️","tokens_out":8612,"duration_ms":69214,"temperature":0.7,"pith_summary":"Small systematic gate over-rotations, a leading source of error in quantum processors, are usually assumed to be faint: weak but present in the data. This paper argues that when measured through the cheapest output a device provides—a single fixed-basis histogram—such a coherent error is absent, not faint: to first order it leaves the histogram unchanged, so the Fisher information is singular, the Cramér–Rao bound is infinite, and no estimator recovers it no matter how many shots are taken. The impossibility is exact at zero angle for commuting single- and two-qubit transverse over-rotations with known support on the canonical input, where each coherent angle lies in the Fisher kernel. The paper further proves that a fixed set of ⌈log2(n+1)⌉ extra measurement settings makes every such fault visible, that this count is minimal among product-Pauli augmentations, and that the finite-sample cost is governed by conditioning, not coverage, with a closed-form floor. A sympathetic reader cares because this moves the answer from 'collect more data or enrich the model' to 'design the measurement,' and gives an explicit design that attains the floor.","feed_headline":"Coherent qubit noise is absent, not faint, from one histogram","feed_subtitle":"A logarithmic set of extra measurement settings restores the invisible signal and sets a closed-form conditioning floor.","key_machinery":"The coherence veil: the kernel KZ of the classical Fisher information of the single Z-histogram, the subspace of parameter directions the histogram cannot resolve at any sample size. Its closed form is an incidence rank formula rank(JZ)=rank(BΩ)+rank((I−PB)H), with explicit exchange basis v(u)=(u, (1/2)d⊙c(u)): each veiled direction pairs a coherent over-rotation against the stochastic flip that exactly cancels its effect on the histogram. The argument runs on the extended singular Cramér–Rao bound, whose +∞ branch makes non-estimability a theorem rather than a heuristic. The cure is a separating code: assign each qubit a distinct nonzero binary codeword and read the corresponding X/Y settin","core_discovery":"At η=0, for commuting weight-1 and weight-2 transverse over-rotations with known support on a Z-diagonal input, every coherent angle lies exactly in the Fisher kernel of a single Z-basis histogram: its singular Cramér–Rao bound is infinite, and no finite-variance, locally unbiased, first-order estimator recovers it at any sample size. The kernel has a closed-form rank formula, and each veiled direction pairs a coherent move u with the compensating stochastic move (1/2)d⊙c(u). A generic nonzero angle partially lifts the veil; beyond four qubits the obstruction becomes conditioning rather than rank. The cure is measurement design: a fixed set of ⌈log2(n+1)⌉ product-Pauli settings restores iden","pith_inferences":["The same kernel-check diagnostic transfers to any fixed-measurement inverse problem: a target in the kernel of the averaged Fisher information is unrecoverable from passive data, and only a measurement change (or input change) can help. Applying this test to a classical linear inverse problem would be a direct, low-cost validation of the paper's transferable rule.","The ⌈log2(n+1)⌉ count is the group-testing bound; the paper leaves open whether entangled or adaptive measurements could lift the veil at η=0 with fewer settings. Answering that would sharpen the minimality statement beyond product-Pauli augmentations.","The closed-form floor suggests a crossover: at small n the fixed-setting code is the cheaper intervention, but the (1−2p)^n branch decays exponentially in n, so at scale an active twirling protocol that removes the coherent angle should become more shot-efficient. The paper's scaling remarks imply this; it is not a proved recommendation.","For non-commuting generators (always-on ZZ crosstalk), the first-order code leaves a residual second-order veil; quantifying how many additional settings a second-order Fisher analysis requires would be a natural follow-up, and the paper names this as an open problem."],"forward_implications":["Adding a coherent parameter to a Z-only model cannot recover the angle at η=0; in simulation the enriched single-histogram estimator pays 12–67× the mean-squared error of the separating-code design at equal shots.","A fixed design of ⌈log2(n+1)⌉ extra product-Pauli settings lifts the veil for every known-support commuting weight-1/2 transverse family, and for the complete family this count is minimal at η=0 among product-Pauli augmentations of Z^n.","Once coverage holds, finite-sample recovery error is set by the design's smallest singular value, not by coverage: across 250 (n=3) and 120 (n=4) full-rank designs, RMSE tracks σmin (Spearman −0.63/−0.85) and worst-conditioned quintiles pay 3.1–4.1× the RMSE of the best at equal budget.","Below coverage the worst-direction sample complexity diverges as Ω(η^{−2}) as η→0, so the closer a device is to calibrated, the worse a blind single-basis measurement performs.","On superconducting hardware with injected errors, the single fixed-basis fit is 3–5× more biased than the separating-code fit, consistent with the predicted conditioning ordering."],"fun_headline_variants":["Coherent noise is absent, not faint—fix with log extra settings","From faint to absent: log many extra settings reveals qubit noise","Log extra settings cure absent coherent noise that stymies histograms","Invisible coherent noise becomes visible with log many Pauli settings","Absent noise not faint: logarithmic measurement design reveals it"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The pre-noise probe is Z-diagonal (canonically |0^n⟩), so odd-Y Pauli expectations vanish; if the input carried Y-coherence, the single histogram would partially expose the coherent angle, and the 'absent' claim and the logarithmic cure would change.","fun_headline_variants_meta":{"raw":{"variants":["Coherent noise is absent, not faint—fix with log extra settings","From faint to absent: log many extra settings reveals qubit noise","Log extra settings cure absent coherent noise that stymies histograms","Invisible coherent noise becomes visible with log many Pauli settings","Absent noise not faint: logarithmic measurement design reveals it"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00054,"raw_usage":{"total_tokens":2482,"prompt_tokens":855,"completion_tokens":1627,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":599,"completion_tokens_details":{"reasoning_tokens":1538}},"tokens_in":599,"tokens_out":1627,"duration_ms":13746,"temperature":1.0,"reasoning_tokens":1538,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T09:16:52.039479+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Prepare |0^n⟩ with a single known over-rotation of angle η on one qubit and measure the Z-basis histogram at η=0 and at small η: the claim predicts the histogram's first-order derivative with respect to η is exactly zero at η=0 (the Fisher column vanishes), while a generic nonzero angle gives a small but nonzero slope. Equivalently, prepare the same over-rotation on an input with Y coherence (e.g., |+⟩ rotated by a small phase) and measure a single Z histogram: the paper's mechanism predicts the coherent angle immediately becomes visible from that single histogram, since the odd-Y expectation","supporting_citations":[],"review_version":1}