{"id":"16a255f7-2c74-4671-bf2f-a17e324c29a0","arxiv_id":"2607.27025","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"A tripartite QNDM protocol certifies path interference on one detector while a second detector emits near-uniform three-outcome random numbers without requiring spacelike separation.","lead":"A quantum random-number generator uses one system and two detectors so that one detector certifies genuine quantum interference while the other emits nearly uniform random outcomes at the same time. Because certification needs no spacelike separation, the design is aimed at compact, scalable devices rather than lab-scale Bell tests.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Semi-DI min-entropy bound is derived inside the assumed QNDM model; observed P_ND negativity alone does not rigorously cap D2 bias without dimension/coupling assumptions.","rationale":"The reader correctly flagged trusted detector measurements plus the imported “negativity ⇒ unfakeable path superposition” claim as the soft spot. The sharper load-bearing gap is that the entropy bound is a within-model calculation, not a reduction from observed negativity alone; the paper’s explicit claim that dimension assumptions are unnecessary is unsupported. That keeps the work a coherent theory proposal with a useful simultaneous cert+gen architecture and an internally consistent trade-off, but not yet a proven source-independent QRNG. No internal algebraic contradiction turned up in the reduced states, the P_q sum rule, or the optimized example; the issue is the scope of the security claim. Verdict stays CONDITIONAL on a clearer (ideally dimension-bounded or device-characterized) security definition and eventual experiment—the same place the reader landed.","tokens_in":15973,"tokens_out":624,"duration_ms":67424,"concrete_test":"Construct or rule out a classical mixture or higher-dimensional source that, under the same trusted measurements reconstructing G_λ on D1 and β∈{0,±2} on D2, matches Fig. 2a negativity at |P_q(−1)|≈0.06 while achieving max_β P_β(λ*)>1/3+|P_q(−1)| for some sampled λ*. If such a strategy exists, the source-independent reading of Eq. (5) fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline security claim is that D1 negativity plus Eq. (5), H_min(X)≥LK log(3/(1+3|P_q(−1)|)), certifies randomness against source manipulation, and that the user needs “not even … assumptions on the state dimensions.” The bound and the key identities P_q(β=0)=cos(λ_l)P_q(−1), P_q(β=2)=−cos(λ_l)P_q(−1) (Appendix, after (S22)–(S24)) are obtained only inside the fixed model: 3-level S, commuting â/ with the stated spectra, couplings U1/U2, and the path-degeneracy structure that links A_4,7 to β=0. The appendix never proves that an arbitrary source—higher-dimensional, or adversarially correlated with the detectors—that reproduces the same observed G_λ (hence the same |P_q(−1)|) is forced to obey the same D2 bias. Without that reduction, negativity is a quantumness witness under trusted D1/D2 readouts, not a model-independent cap on p_guess(X). The semi-DI / source-independent label therefore overreaches what is shown.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper proposes a QRNG based on a tripartite quantum non-demolition measurement setup: a three-level system S coupled to a two-level detector D1 and a three-level detector D2. D1 reconstructs a quasi-probability P_ND whose negativity certifies path superposition, while D2 simultaneously emits outcomes β∈{0,±2} whose λ-averaged distribution can be optimized near uniformity. A min-entropy bound H_min(X)≥LK log(3/(1+3|P_q(−1)|)) links extractable randomness to certified negativity. An optimized spin-1 example achieves relative min-entropy deficit ~9.81% (bound δ≈15.2% at |P_q(−1)|≈0.06). Certification needs no spacelike separation. The protocol is presented as semi-device-independent/source-independent with trusted detector measurements.","tokens_in":18369,"tokens_out":1259,"duration_ms":49762,"significance":"If the construction and scoped security claims hold, this is a practically relevant alternative to Bell and Leggett–Garg QRNGs: simultaneous generation and certification without spatial separation, plus an explicit trade-off between quasi-probability negativity and min-entropy. The unitary evolution, reduced detector states, path indexing,  degeneracy, and P_q(β)↔P_q(Δ) identities are derived carefully in the text and Appendix. The optimization example is concrete. Even with a narrower security model, the architecture contributes to semi-DI randomness and to applications of QNDM witnesses.","major_comments":[{"comment":"The source-independent/semi-DI claim overreaches what is proven. The text says the user need not know preparations “not even … assumptions on the state dimensions,” and that Eq. (5) certifies randomness against source manipulation. The bound and identities P_q(β=0)=cos(λ_l)P_q(−1), P_q(β=2)=−cos(λ_l)P_q(−1) (Appendix after S22–S24) hold only inside the fixed model: 3-level S, stated â/ spectra, U1/U2 couplings, and path degeneracy tying A_4,7 to β=0. No reduction shows an arbitrary source reproducing the observed G_λ must obey the same D2 bias. Restate security to match trusted readouts and model assumptions, or supply a proper reduction.","section":"Random number generator; Eq. (5); Appendix (S17)–(S31)"},{"comment":"Security against classical spoofing of P_ND negativity under this protocol is imported from prior QNDM work [21,22] without a self-contained argument for these couplings and finite (L,K) sampling. The claim that negative regions cannot be reproduced by a classical device sampling a probability distribution must address D2’s decoherence functional f(n,k) and finite Fourier sampling of G_λ. A short classical-simulation bound under trusted readouts is needed for certification to be load-bearing here.","section":"System and set-up; Eqs. (3)–(4); P_ND decomposition"},{"comment":"The trusted vs untrusted partition is under-specified for a semi-DI claim. The paper notes that “measurements of detectors D1 and D2 need to be trusted,” yet still frames the protocol as source-independent in the sense of Refs. [24,25]. Clarify in one place which operations are trusted (D1/D2 measurements, couplings, dimensions) and which are untrusted (source state and û), and what adversarial power observed negativity alone rules out.","section":"Random number generator; Conclusions"}],"minor_comments":[{"comment":"Figure 2 caption/panel labels are hard to parse in the manuscript rendering. Ensure the published figure clearly separates P_ND(Δ) from P̄_β and reports the numerical parameters.","section":"Fig. 2"},{"comment":"The mapping n=1+3(i+1)+(j+1) is dense; a small table of (i,j)↔n, α_n, β_n would help verify degeneracy β∈{0,±2} and the identification of A_4,7, A_5,8, A_6,9.","section":"System and set-up; Appendix"},{"comment":"In Application/Conclusions, “more than 90% … genuinely random” should be tied explicitly to ΔH_min/H̄_min∼9.81% versus the looser δ≈15.2% bound.","section":"Application; Conclusions"},{"comment":"Typos: “a posteriorion” → “a posteriori on”; occasional ρ_f vs ρ̄_f switches; M in U2 is not fixed numerically in the example.","section":"Introduction; Eqs. (1)–(2)"},{"comment":"Brief comparison of rate and entropy per shot with LGI QRNGs [15,16] and photonic source-independent QRNGs would better position the practical gain.","section":"Introduction; Conclusions"}],"recommendation":"major_revision","confidential_remarks":"The QNDM-to-QRNG architecture is interesting and likely publishable after security language is aligned with the proofs. Main risk is over-claiming “source-independent” in title/abstract versus DI/semi-DI standards the appendix does not meet. With a trusted-measurement, fixed-dimension framing the technical content is solid. Good fit for a quant-ph/QIP venue once revised."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The useful core here is architectural: they split QNDM certification onto a two-level detector D1 and randomness onto a three-level D2 so generation and path-superposition witness run at the same time, without spacelike separation. That is a genuine step past the LGI-QRNG line they cite, and it sits cleanly on their earlier quasi-probability work.\n\nWhat they do well is the internal math. Path indexing, reduced detector states, the G_λ → P_ND decomposition, the degeneracy of  that forces β ∈ {0, ±2}, the identity P_q(−1)+P_q(1)+P_q(3)=0, and the explicit link that makes the quantum part of P_β proportional to cos(λ) P_q(−1) are all written out and checkable. The lower bound H_min ≥ LK log(3/(1+3|P_q(−1)|)) is a legitimate trade-off inside that model, and the optimized spin-1 example (nearly flat λ-averaged bar P_β, ~10% entropy hit at |P_q(−1)|≈0.06) shows the numbers can be made attractive. Citations are appropriate; self-cites are to the framework they are applying, not circular redefinitions.\n\nThe soft spot is the security language, and the stress-test is right about it. Everything that caps p_guess is derived under fixed dimensions, commuting spectra, and the stated couplings. Observing the same G_λ (hence the same |P_q|) does not, by itself, force an arbitrary higher-dimensional or adversarially correlated source to obey the same D2 bias. They also state plainly that D1 and D2 measurements must be trusted. So this is a trusted-detector, model-dependent quantumness witness plus an optimized generator, not yet a full source-independent or composable semi-DI proof. No experiment, no code—fine for a theory proposal, but the abstract’s “semi-device-independent” and “no assumptions on state dimensions” phrasing should be tightened.\n\nWho it is for: people building temporal/semi-DI QRNGs and anyone already using QNDM witnesses. Worth a serious referee; the construction and the entropy calculation are real enough to publish after the security claims are scoped to what is actually shown. I would engage.","headline":"Solid dual-detector QNDM QRNG idea with clean algebra and a real min-entropy trade-off; the semi-DI/source-independent security claim overreaches what the model actually proves.","tokens_in":16979,"tokens_out":589,"would_cite":true,"duration_ms":11935,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A tripartite non-demolition setup certifies quantum path superposition on one detector while a second detector emits near-uniform three-outcome random numbers at the same time, without needing spacelike separation.","keywords":["quantum random-number generator","quantum non-demolition measurement","semi-device-independent","quasi-probability distribution","path superposition","min-entropy","Leggett-Garg"],"falsifier":"Build the proposed three-level system plus two detectors, reconstruct P_ND from D1 while collecting D2 strings, and check whether clear negativity appears together with a near-uniform three-outcome average and min-entropy consistent with the stated bound; absence of negativity when the designed unitary and state should produce it, or classical spoofing of the same negativity under the actual couplings, would refute the claim.","tokens_in":16809,"feed_emoji":"🎲","tokens_out":932,"duration_ms":19154,"temperature":0.7,"pith_summary":"The paper proposes a quantum random-number generator built from one three-level system coupled to two detectors (two-level and three-level) under sequential quantum non-demolition measurements. One detector reconstructs a quasi-probability distribution over evolution paths; negativity in that distribution certifies coherent path superposition and therefore genuine quantum dynamics. The other detector simultaneously produces outcomes from a three-value alphabet whose average distribution can be tuned near uniform by choice of initial state and unitary, so the min-entropy of the output string stays close to the maximum. Generation and certification happen in the same runs, and certification does not require spacelike separation of devices. That removes a major barrier of Bell-based device-independent generators and points toward compact, integrable hardware while still giving a semi-device-independent guarantee against source manipulation, provided the detector measurements themselves are trusted.","feed_headline":"One chip certifies quantum randomness without space-like separation","feed_subtitle":"Two detectors share a non-demolition run: negativity proves quantum paths, the other emits near-uniform bits","key_machinery":"The quantum non-demolition measurement quasi-probability distribution P_ND(Δ) = P_cl + P_q reconstructed from D1: negativity of P_q is treated as a necessary and sufficient signature of path superposition that a classical probability source cannot reproduce, while the same couplings set the three-outcome statistics of D2.","core_discovery":"In a QNDM tripartite architecture, detector D1’s reconstructed quasi-probability P_ND certifies path superposition via negativity while detector D2 simultaneously emits outcomes β in {0, ±2} whose λ-averaged distribution can be optimized near-uniform. The min-entropy of the full string is lower-bounded by LK log(3/(1+3|P_q(−1)|)), and an optimized spin-1 example reaches about 90% of maximal extractable randomness while still showing clear negativity.","pith_inferences":["Because certification and generation share the same physical runs, finite-sample statistical tests of negativity directly bound the usable randomness rate in real time.","Integrated platforms that already support spin-1 or qutrit control (cold atoms, superconducting circuits, NV centers) are natural first testbeds for a proof-of-principle device.","If classical models can reproduce the observed P_ND negativity under realistic noise and finite L, the semi-DI security argument would need an explicit noise-tolerant reformulation."],"forward_implications":["Randomness generation and quantum certification can run on the same compact chip without spacelike-separated modules.","Initial state and unitary can be tuned to trade a controlled amount of min-entropy for stronger negativity certification.","Adding further non-demolition couplings or higher-dimensional detectors is predicted to enlarge the outcome alphabet and improve extractable randomness.","The protocol supplies a concrete semi-device-independent (source-independent) QRNG route that needs no input random seed."],"fun_headline_variants":["QNDM tripartite setup certifies randomness without spacelike separation","One detector flags negativity while the other emits near-uniform trits","Semi-device-independent QRNG runs certification and generation together","Spin-1 QNDM protocol reaches ~90% max entropy with clear negativity","Non-demolition dual-detector chip shrinks quantum RNG constraints"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The security claim rests on trusting the measurements of both detectors and on the assertion that observed negativity in the quasi-probability cannot be faked by a classical device sampling a genuine probability distribution.","fun_headline_variants_meta":{"raw":{"variants":["QNDM tripartite setup certifies randomness without spacelike separation","One detector flags negativity while the other emits near-uniform trits","Semi-device-independent QRNG runs certification and generation together","Spin-1 QNDM protocol reaches ~90% max entropy with clear negativity","Non-demolition dual-detector chip shrinks quantum RNG constraints"]},"model":"grok-4.5","effort":"low","cost_usd":0.004884,"raw_usage":{"total_tokens":1343,"prompt_tokens":739,"num_sources_used":0,"completion_tokens":77,"cost_in_usd_ticks":48844000,"prompt_tokens_details":{"text_tokens":739,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":527,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":739,"tokens_out":77,"duration_ms":9749,"temperature":1.0,"reasoning_tokens":527,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-30T13:25:36.660555+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Build the proposed three-level system plus two detectors, reconstruct P_ND from D1 while collecting D2 strings, and check whether clear negativity appears together with a near-uniform three-outcome average and min-entropy consistent with the stated bound; absence of negativity when the designed unitary and state should produce it, or classical spoofing of the same negativity under the actual couplings, would refute the claim.","supporting_citations":[],"review_version":1}