{"id":"93cbc57e-c1fc-4f7b-b44d-c38263ab77e0","arxiv_id":"2602.15966","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"For a controlled-rotation probe, gate-sequence leakage is predicted to peak at θ*(k)=2 arcsin(√(2/(k+2))), but the paper provides neither a derivation of the envelope nor the experimental data supporting the prediction.","lead":"This paper models a quantum side-channel where an eavesdropper's probe qubit couples to a victim's gates, and learns to decode the hidden gate sequence from the probe's measurement histogram. It predicts a depth-dependent 'Goldilocks' coupling strength for leakage, but the analytic claims are asserted rather than derived and the experimental validation is not shown.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (8) is an asserted proxy rather than a derived envelope; θ*(k) is the maximizer of an assumed curve, and the k=1 case already contradicts the claimed cos^k form.","rationale":"The reader's weakest assumption identifies exactly the load-bearing issue: the analytic predictor rests on asserted functional forms, and the paper provides no derivation, code, or quantitative data. My independent read agrees. The k=1 counterexample strengthens the case: the envelope form Eq. (8) is not a universal consequence of the controlled-Rx dynamics, since a direct one-step calculation lacks the cos(θ/2) factor. The absence of any derivation for Eqs. (6)–(8) means θ*(k) is not a physical prediction but a fitted curve, so the central claim that strict recovery 'should concentrate' at the predicted coupling band is unsupported. A numerical test of exact distinguishability could settle this: if the exact argmax ridge matches Eq. (9) across depths, the proxy would be vindicated; if not, the central claim fails. Because the reader already recommends REJECT on this basis, no verdict adjustment is needed.","tokens_in":10739,"tokens_out":7338,"duration_ms":74711,"concrete_test":"Simulate the exact noiseless two-qubit circuit of Sec. III-B for k=1,...,10 over a fine θ grid in [0,2π]. For each (k,θ), compute the exact pairwise total-variation distances D_TV(P_g, P_{g'}) between full probe distributions for all gate strings, or the class-mean separation of Eq. (5). Then: (i) for k=2, check whether all pairwise distances vanish at some isolated θ₀ as Eq. (7) claims; (ii) for each k, locate the argmax of the minimum/mean pairwise TV and compare it with θ*(k) from Eq. (9). If the argmax deviates by more than a few degrees, or if no common θ₀ exists at k=2, then Eqs. (6)–(9) are not supported by the stated controlled-Rx dynamics.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim is Eqs. (8)–(9): Δp_k ≈ α_G sin²(θ/2) cos^k(θ/2), whose maximizer θ*(k) = 2 arcsin√(2/(k+2)) is presented as predicting where strict recovery concentrates. But the paper itself calls Eq. (8) 'a useful analytic proxy' and gives no derivation from the controlled-Rx instrument. The cos^k contraction factor is asserted, and the 'alphabet-dependent scale' α_G is not specified as a function of k or θ. Thus the predictor is the maximizer of an assumed curve, not a consequence of the stated dynamics. This is load-bearing because the abstract claims to 'derive a depth-dependent leakage envelope' and the results sections treat Eq. (9) as a quantitative prediction. A concrete inconsistency: for k=1, the proxy gives Δp_1 ∝ sin²(θ/2)cos(θ/2), whose maximizer is θ=π, whereas a direct one-step computation of the probe outcome-1 probability gives p_1 = sin²(θ/2) sin²(φ/2), so the gate-conditioned spread has no cos(θ/2) factor. The paper does not report k=1, but the claimed depth dependence is meant to be general. Additionally, Eqs. (6)–(7) assert a factorization A₂ ∝ sin²(θ/2)κ₂(θ;G) with isolated zeros, but no explicit κ₂ or θ₀ is computed, and the statement that sin²(θ/2) is π-periodic is false (its period is 2π). The experimental validation is described only qualitatively, with no numeric results, code, or data to confirm that the ridge actually tracks Eq. (9).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a sequential coherent side-channel model in which an adversarial probe qubit couples to Alice's qubit after each hidden gate and is measured mid-circuit, yielding a full-correlation histogram over probe bit-strings. After presenting a general coupling- and measurement-agnostic framework, it specializes to a controlled-Rx(θ) probe with a commuting Rx gate alphabet and claims a depth-dependent leakage envelope Δp_k ≈ α_G sin²(θ/2) cos^k(θ/2), whose maximizer θ*(k) = 2 arcsin√(2/(k+2)) predicts a 'Goldilocks' coupling band. The paper also trains a temporal convolutional network decoder that maps full-correlation histograms to gate labels across a grid of coupling and noise parameters. Results are reported as qualitative heatmaps for k=2 and k=7, showing a coupling ridge, noise narrowing, and finite-shot scaling.","tokens_in":11206,"tokens_out":5448,"duration_ms":49523,"significance":"The question of when a coherent probe record enables strict sequence recovery is timely and relevant to multi-tenant quantum processors. The full-correlation observation model is a sensible primitive, and the idea of an amortized decoder conditioned on physical parameters is promising. If the analytic predictor were actually derived from the controlled-Rx dynamics and validated quantitatively, the paper would provide a useful design rule for side-channel risk and a concrete baseline for future work. However, the central quantitative claim is not derived from the stated dynamics, is contradicted by a direct calculation at k=1, and the experimental evidence is qualitative only. In its current form, the significance is not established.","major_comments":[{"comment":"The central predictor θ*(k) is obtained by maximizing f_k(θ)=sin²(θ/2)cos^k(θ/2), but Eq. (8) is explicitly introduced as 'a useful analytic proxy' and the alphabet-dependent scale α_G is never specified. No derivation from the controlled-Rx instrument of Sec. III-B is given for the cos^k contraction factor. The claimed depth dependence fails already at k=1: for a single Rx(φ) gate and target initialized in |0>, the probe outcome-1 probability is p_1 = sin²(θ/2)sin²(φ/2), so the gate-conditioned spread over the alphabet has no cos(θ/2) factor. Thus the maximizer of the proxy is not the maximizer of the actual spread, and Eq. (9) is not a physical prediction derived from the dynamics.","section":"§V, Eqs. (8)–(9)"},{"comment":"The depth-2 factorization A₂ ∝ sin²(θ/2)κ₂(θ;G) and the existence of isolated zeros of κ₂ are asserted without deriving κ₂ or computing θ₀. The implication in Eq. (7) that κ₂(θ₀;G)=0 implies D₂(u,u′)=0 for all pairs requires that A₂ fully characterizes the pairwise distinguishability of the two-step probe laws; no such equivalence is shown. As a result, the 'blind-spot' prediction is not established.","section":"§IV-B, Eqs. (6)–(7)"},{"comment":"The experimental validation is qualitative only. No numerical values of strict-sequence accuracy are reported, no error bars or confidence intervals are given, and no table quantifies accuracy as a function of θ, λ, and N. The captions state that the ridge aligns with θ*(d), but the underlying data and code are not provided, so the claim that Eq. (9) tracks the ridge cannot be independently checked. The same applies to the noise-narrowing and shot-scaling statements in §VIII-b,c.","section":"§VIII, Figs. 2–3"},{"comment":"The sentence 'irrespective of whether Eve uses marginals or full correlations' is not justified. The envelope Δp_k is a per-step marginal quantity, while the distinguishability measure D_d(u,u′) in Eq. (5) is defined on full distributions. No argument is given that the full-correlation distinguishability shares the same maximizing coupling, so this assertion is unsupported.","section":"§V, last paragraph"}],"minor_comments":[{"comment":"The text states that sin²(θ/2) is π-periodic; this is mathematically false. sin²(θ/2) has period 2π, not π. The intended statement may refer to sin²(x), but as written it is incorrect.","section":"§IV-B"},{"comment":"The dimension notation 'R^{2+k+2k}' appears to be a typo. Since x ∈ R^{2^k}, the feature vector X_t should be in R^{2 + k + 2^k}, not R^{2+k+2k}.","section":"§VI-A, Eq. (11)"},{"comment":"The notation mixes depth subscripts: ar P_{k,u} is defined with k, while D_d is written with d, and both are used for the same depth variable. This is confusing and should be unified.","section":"§IV, Eqs. (4)–(5)"},{"comment":"Figures 2 and 3 are referenced but their actual images are not present; captions alone cannot support the quantitative claims made in the text. Axis labels and color scales are also missing.","section":"§VIII"},{"comment":"Reference [32] is 'in preparation.' Deferring extensions and additional derivations to a future manuscript is not a substitute for presenting the necessary derivations and data here.","section":"§VII"}],"recommendation":"reject","confidential_remarks":"The paper appears to be an early-stage preprint. The main analytic result is unsupported and contradicted by a direct calculation at k=1, and the experimental section contains no quantitative data or code. I recommend rejection. A future resubmission might be viable if the analytic claims are either re-derived from the actual dynamics or replaced by an explicitly empirical predictor, and if the experiments are reported with full numerical results, error bars, and reproducibility information."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Let me get straight to it: the paper's real new content is the specific predictor θ*(k) = 2 arcsin√(2/(k+2)) and the depth-2 blind-spot claim for a controlled-rotation probe with a commuting Rx alphabet. I haven't seen that envelope in the crosstalk side-channel literature, and it's worth a look. The full-correlation histogram framing is standard (it's the sufficient statistic for i.i.d. shots), so that's not the novelty. The envelope and the generalization claim are.\n\nWhat the paper does well: the threat model is clean, the authors are honest about what \"hardware-agnostic\" does and doesn't mean, and the point that full correlations can improve sample efficiency but can't create information where the physics has suppressed distinguishability is sensible. Restricting to a commuting alphabet to isolate measurement back-action is a defensible first step.\n\nBut the load-bearing parts don't hold. Eqs. (6)–(8) are asserted, not derived; the paper itself calls Eq. (8) \"a useful analytic proxy,\" yet the abstract says the envelope is \"derived\" and the results treat θ*(k) as a prediction. That gap is real. The stress-test note lands: for k=1, a direct computation gives p_1 ∝ sin²(θ/2) sin²(φ/2) with no cos(θ/2) factor, so the proxy's maximizer (~109°) doesn't match the physical one (π). That concrete mismatch shows the proxy is a guessed functional form, not a consequence of the controlled-Rx instrument. The κ2 factorization is similarly uncomputed — no explicit κ2, no θ0 — and the claim that sin²(θ/2) is π-periodic is wrong (period 2π). Minor, but symptomatic.\n\nThe experimental side is the other soft spot. Figures 2–3 are described only qualitatively: no numeric accuracy values, no error bars, no tables, no code or data. For a paper whose central claim is that the empirical ridge tracks Eq. (9), that's a serious omission. You can't verify the alignment.\n\nSo the reader's REJECT is justified. The path to conditional is clear: derive Eqs. (6)–(8) exactly for small k (at least k=1,2), compute κ2 explicitly, and release code plus quantitative accuracy curves with error bars. If that lands, this becomes a credible secondary result for quantum cloud security.\n\nI'd still send it to referees rather than desk-reject — the topic matters, the formula is checkable, and a competent referee could quickly decide whether the proxy is derivable or fake. But as submitted, it's not acceptable. Workshop-level, needs substantial revision.","headline":"The core claim — a depth-dependent coupling ridge θ*(k) for controlled-Rx probes — is new but rests on an asserted proxy, not a derivation, and the experiments are only described qualitatively; reject as is, but the topic and specific formula deserve referee scrutiny.","tokens_in":11620,"tokens_out":3180,"would_cite":false,"duration_ms":33497,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P94"],"pacs":["03.67.-a"],"model":"deepseek-v4-flash","headline":"A closed-form formula predicts the coupling strength at which an adversary's probe qubit can reliably recover a hidden quantum gate sequence.","keywords":["quantum side-channel","sequential coherent leakage","full-correlation histogram","controlled-rotation coupling","Goldilocks coupling band","depolarizing noise","gate-sequence recovery","temporal convolutional network"],"falsifier":"Simulate the exact (no-envelope) probe distributions for the controlled-Rx coupling at depths 2 and 3 over a fine θ grid, and check whether the depth-2 total-variation distance between two chosen sequences hits zero at the predicted blind-spot couplings and whether the empirical strict-recovery ridge for many random sequences tracks θ*(k) to within finite-shot error bars. A mismatch between the exact TV computation and the envelope's ridge would falsify the predictor as a physical law.","tokens_in":10633,"feed_emoji":"⚛️","tokens_out":5885,"duration_ms":54009,"temperature":0.7,"pith_summary":"The paper argues that an adversary who repeatedly couples a probe qubit to a target qubit during a hidden gate sequence can learn the gates—but only when the coupling strength sits in a narrow depth-dependent band, not in the naive limits of very weak or very strong coupling. For a controlled-rotation coupling and a commuting gate alphabet, it derives a closed-form predictor, θ*(k)=2arcsin(√(2/(k+2))), for the center of that band, and shows experimentally that strict sequence recovery concentrates there. The key observational choice is the full-correlation histogram over probe bitstrings, which the paper treats as the adversary's sufficient statistic and feeds to a parameter-conditioned neural decoder that recovers per-step gate labels across a grid of coupling and noise settings without retraining. The paper also identifies exact 'blind spots' at depth 2 where pairs of sequences become information-theoretically indistinguishable. The broader claim is that coherent side-channel risk is a landscape over coupling, noise, shot count, and depth, not a single monotone leak rate.","feed_headline":"Formula pinpoints the coupling where quantum gate secrets leak","feed_subtitle":"The leak is not monotone: an adversary recovers a hidden gate sequence only in a narrow depth-dependent band, and the paper gives its center","key_machinery":"The central object is the empirical full-correlation histogram bPg(b), the joint distribution of probe outcomes over bitstrings b∈{0,1}^k, which is the sufficient statistic for Eve's classical post-processing. The argument is carried by the envelope proxy Δp_k(θ;G) ≈ α_G sin²(θ/2) cos^k(θ/2) and the depth-2 factorization A2 ∝ sin²(θ/2)κ2(θ;G); the former maximizes to give θ*(k), the latter supplies the isolated blind-spot couplings. Together these convert a high-dimensional inference problem into a one-parameter ridge.","core_discovery":"For the controlled-rotation probe with a commuting Rx gate alphabet, the paper claims that strict recovery of Alice's per-step gate labels from the probe's full-correlation histogram is governed by a depth-dependent envelope, and that the coupling strength maximizing distinguishability is exactly θ*(k)=2arcsin(√(2/(k+2))). This predictor locates the ridge of strict recovery in coupling sweeps, irrespective of whether Eve uses marginals or full correlations, because the physical distinguishability, not sample efficiency, is the bottleneck. At depth 2, the gate-dependent amplitude factorizes as sin²(θ/2)κ2(θ;G), and κ2 has isolated zeros that make all sequences indistinguishable at those speci","pith_inferences":["If the envelope proxy reflects a general tradeoff between per-step transfer and depth-k contraction, analogous closed-form predictors should exist for other probe couplings; testing this on a diagonal coupling would separate the universal mechanism from the specific alphabet-dependent modulation.","The depth-2 factorization suggests a testable algebraic structure: the zeros of κ2 should coincide with the zeros of the exact two-step instrument's gate-dependent part, so a symbolic computation of the two-step channel would settle whether the blind spots are exact or merely proxy-level.","For random (non-commuting) gate alphabets, back-action and measurement order interact differently, so the predictor's ridge may shift; the same histogram-based decoder could be applied to see whether the Goldilocks shape persists.","The paper's landscape view—leakage as a function of (θ,λ,N,k)—implies that defenders in a multi-tenant machine could schedule jobs at couplings far from θ*(k) to reduce side-channel risk, though the operational cost of doing so is left unquantified."],"forward_implications":["Strict sequence recovery concentrates in a coupling band whose center is θ*(k)=2arcsin(√(2/(k+2))); deeper circuits require weaker couplings.","Full-correlation records improve sample efficiency at low shots but do not extend the recoverable regime beyond the predicted band, since the bottleneck is physical distinguishability, not statistics.","Depolarizing noise narrows the band and lowers accuracy, so noise and coupling trade off; operating outside the band keeps accuracy near the random-guess baseline even with unlimited shots.","At depth 2, isolated couplings exist at which all pairs of sequences are information-theoretically indistinguishable, and noise broadens these into low-accuracy bands.","A single decoder conditioned on (θ,λ) suffices to predict gates across the whole grid, indicating the learned map internalizes the physical parameter dependence."],"fun_headline_variants":["Quantum gate secrets leak only in a narrow coupling band","Depth-dependent band predicts where quantum gates leak","Hardware-agnostic model pinpoints quantum leak window","Narrow coupling band governs quantum gate leakage","Quantum side-channel leaks only at specific depths and couplings"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The predictor and blind-spot structure are derived from two asserted functional forms—the depth-2 factorization A2 ∝ sin²(θ/2)κ2(θ;G) with κ2's zeros, and the envelope Δp_k ≈ α_G sin²(θ/2)cos^k(θ/2)—which the paper calls 'useful analytic proxies' and does not derive from the controlled-Rx unitary; if either form is not forced by the dynamics, θ*(k) is an assumed curve rather than a physical prediction.","fun_headline_variants_meta":{"raw":{"variants":["Quantum gate secrets leak only in a narrow coupling band","Depth-dependent band predicts where quantum gates leak","Hardware-agnostic model pinpoints quantum leak window","Narrow coupling band governs quantum gate leakage","Quantum side-channel leaks only at specific depths and couplings"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000153,"raw_usage":{"total_tokens":1059,"prompt_tokens":775,"completion_tokens":284,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":519,"completion_tokens_details":{"reasoning_tokens":225}},"tokens_in":519,"tokens_out":284,"duration_ms":3188,"temperature":1.0,"reasoning_tokens":225,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T22:42:36.348517+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the exact (no-envelope) probe distributions for the controlled-Rx coupling at depths 2 and 3 over a fine θ grid, and check whether the depth-2 total-variation distance between two chosen sequences hits zero at the predicted blind-spot couplings and whether the empirical strict-recovery ridge for many random sequences tracks θ*(k) to within finite-shot error bars. A mismatch between the exact TV computation and the envelope's ridge would falsify the predictor as a physical law.","supporting_citations":[],"review_version":1}