{"id":"be51b225-4e34-4ea1-8a84-9ee0d41e478b","arxiv_id":"2606.23231","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Experimental realization of a continuous-variable semi-device-independent QRNG with four-state coherent states and heterodyne detection, certifying 0.223 bits of Shannon entropy per measurement using an integrated photonic receiver.","lead":"The paper demonstrates an experimental quantum random number generator using coherent light states and an integrated detector that certifies 0.223 bits of randomness per measurement under semi-device-independent assumptions. This could support more practical secure randomness sources for quantum communication systems.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"SDP relaxation gap for entropy lower bound under photon-number constraint not quantified","rationale":"Reader's weakest assumption directly identifies the photon-number + SDP step; full-text access does not remove the need to verify relaxation tightness, which is the single internal condition required for the numeric claim to hold. No other inconsistency (e.g., entropy accumulation application) appears more load-bearing from the given description.","tokens_in":1696,"tokens_out":294,"duration_ms":14025,"concrete_test":"Re-solve the SDP (or a higher-order relaxation) for the exact four-state heterodyne scenario with the paper's reported photon-number bound; compare the resulting entropy lower bound to the published 0.223 value. If the new bound is >0.02 bits lower, the headline certification weakens.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The 0.223 bit/measurement certification rests on semidefinite relaxation yielding a sufficiently tight lower bound on the conditional Shannon entropy given only the experimental photon-number constraint (mean photon number or support bound) and the four-state coherent-state constellation. If the relaxation gap is non-negligible, the reported value overestimates the certifiable entropy; the abstract and method description give no duality-gap bound, no comparison to exact SDP or numerical optimization on the same constraint set, and no sensitivity analysis showing how the bound changes with small violations of the photon-number assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript experimentally realizes a continuous-variable semi-device-independent QRNG protocol using a four-state coherent-state constellation symmetrically placed in phase space, measured via an integrated low-loss heterodyne receiver. It certifies 0.223 bits of randomness per measurement—the highest reported for this class—by imposing experimentally verifiable photon-number constraints, computing lower bounds on conditional Shannon entropy via semidefinite relaxation, and applying entropy accumulation to obtain finite-size guarantees without an i.i.d. assumption.","tokens_in":1798,"tokens_out":423,"duration_ms":16630,"significance":"If the reported entropy bounds are tight, the result would establish a practical, high-rate architecture for semi-DI randomness generation that combines commercial transmitter components with integrated photonic detection, while relaxing the need for full device characterization. The combination of photon-number constraints with SDP relaxation and entropy accumulation is a methodological strength that could generalize to other photonic QRNG implementations.","major_comments":[{"comment":"Abstract and methods: the central claim of 0.223 bit/measurement rests on the semidefinite relaxation producing a sufficiently tight lower bound on the conditional Shannon entropy given only the photon-number constraint and the four-state constellation. No duality-gap bound, comparison against an exact SDP or numerical optimization on the same constraint set, and no sensitivity analysis under small violations of the photon-number assumption are provided; if the relaxation gap is non-negligible the certified value would be overestimated.","section":"Abstract/methods"}],"minor_comments":[{"comment":"The description of the integrated heterodyne receiver would benefit from explicit loss figures, bandwidth, and how the photon-number constraint is experimentally bounded (e.g., mean photon number or support).","section":null},{"comment":"Clarify the precise SDP formulation (objective, constraints, and relaxation hierarchy) used to obtain the entropy lower bound; a supplementary file with the solver input would improve reproducibility.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and constructive feedback. We address the single major comment below.","responses":[{"response":"We agree that the manuscript does not supply a duality-gap certificate, a direct comparison to an exact solver or finer discretization, or a sensitivity study for photon-number violations. These omissions leave open the possibility that the reported lower bound on conditional entropy is not tight. In the revised manuscript we will add (i) a numerical comparison of the current SDP relaxation against a discretized convex optimization over the same constraint set and (ii) a first-order sensitivity analysis showing the change in the certified entropy when the photon-number bound is relaxed by a few percent. If the gap remains negligible, the 0.223 bit/measurement figure will be retained with the new supporting data; otherwise the certified value will be adjusted downward.","revision_made":"yes","referee_comment":"[Abstract/methods] Abstract and methods: the central claim of 0.223 bit/measurement rests on the semidefinite relaxation producing a sufficiently tight lower bound on the conditional Shannon entropy given only the photon-number constraint and the four-state constellation. No duality-gap bound, comparison against an exact SDP or numerical optimization on the same constraint set, and no sensitivity analysis under small violations of the photon-number assumption are provided; if the relaxation gap is non-negligible the certified value would be overestimated."}],"tokens_in":1283,"tokens_out":305,"duration_ms":15172,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core result is a working continuous-variable semi-device-independent QRNG that uses a four-state coherent-state constellation, heterodyne detection on an integrated photonic receiver, and photon-number constraints to certify 0.223 bits of Shannon entropy per measurement via semidefinite relaxation plus entropy accumulation. This is presented as the highest value reported so far for this class of protocols, and the setup pairs a simple commercial transmitter with a low-loss integrated receiver.\n\nThe practical side is the real contribution. Photon-number constraints are measurable in the lab, so the assumptions are not purely theoretical. The finite-size treatment without an i.i.d. assumption is also useful for real deployments. The architecture looks straightforward to scale in speed.\n\nThe weak point is the entropy bound itself. The certification rests on an SDP relaxation whose gap to the true minimum is not quantified in the abstract, and no comparison to exact optimization or sensitivity checks appears. If the relaxation is loose, the 0.223 figure overstates what can actually be certified. No raw data, error analysis, or explicit verification of the bound is visible either, so the experimental support cannot be checked from what is given.\n\nThe citation pattern and methods follow standard lines in the semi-DI QRNG literature, with no obvious circularity or invented parameters. The work is internally consistent on its own terms.\n\nThis paper is aimed at groups building practical quantum randomness sources or integrated photonic QRNGs. Readers who need a concrete high-rate implementation with reduced assumptions will find the setup details useful. It deserves peer review because the experimental realization is new and the constraint approach is reproducible in principle, even though the bound validation needs to be shown in full.","headline":"The paper gives an experimental semi-DI QRNG demo with an integrated heterodyne receiver that reaches 0.223 bits per shot, but the SDP relaxation tightness is not shown.","tokens_in":2355,"tokens_out":421,"would_cite":false,"duration_ms":16728,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A four-state coherent-state constellation measured by heterodyne detection certifies 0.223 bits of randomness per shot under photon-number constraints.","keywords":["quantum random number generator","semi-device-independent","heterodyne detection","coherent states","photon-number constraints","entropy certification","integrated photonics","continuous-variable QRNG"],"falsifier":"An experiment that records the heterodyne statistics of the four-state constellation while enforcing the stated photon-number bound and finds that the resulting semidefinite program returns an entropy lower bound materially below 0.223 bits per measurement.","tokens_in":2605,"feed_emoji":"⚛️","tokens_out":703,"duration_ms":17133,"temperature":0.7,"pith_summary":"The paper shows how to certify randomness in a quantum random number generator while assuming only that the source states obey a photon-number limit. It implements the protocol with four coherent states arranged symmetrically in phase space and detects them with an integrated heterodyne receiver. Semidefinite relaxation then produces tight lower bounds on the Shannon entropy extractable from the measurement outcomes. The experiment reaches 0.223 certified bits per measurement, the highest rate reported for any continuous-variable semi-device-independent QRNG. Entropy-accumulation techniques further allow finite-size certification without requiring independent and identically distributed rounds.","feed_headline":"Four-state coherent states certify 0.223 random bits per measurement","feed_subtitle":"Photon-number bounds and semidefinite relaxation enable the highest reported rate for continuous-variable semi-device-independent QRNG.","key_machinery":"Photon-number-constrained semi-device-independent QRNG protocol, in which a bound on the mean photon number of the prepared states is combined with heterodyne detection outcomes and semidefinite relaxation to compute lower bounds on extractable Shannon entropy.","core_discovery":"We realize the protocol using a four-state coherent-state constellation symmetrically distributed in phase space and measured by heterodyne detection, certifying 0.223 bit per measurement, which is the highest value reported to date for a continuous-variable semi-device-independent QRNG. The implementation combines a low-loss integrated photonic heterodyne receiver with a simple transmitter assembled from commercial components, providing a practical and high-speed architecture for semi-device-independent randomness generation.","pith_inferences":["The same photon-number bounding approach could be applied to other continuous-variable protocols to obtain device-independent-style security with modest assumptions.","Integration of the receiver on a photonic chip suggests a path toward compact, mass-producible QRNG modules.","Relaxing the four-state constellation to higher-order modulations might increase the certified rate while preserving the same constraint framework."],"forward_implications":["Finite-size randomness can be certified without assuming independent and identically distributed rounds by combining the bounds with entropy accumulation.","The photon-number constraint is experimentally verifiable and therefore practical for photonic hardware.","The integrated heterodyne receiver and commercial transmitter together form a high-speed, low-loss architecture suitable for real-world deployment.","The achieved rate of 0.223 bits per measurement exceeds all previously reported values for continuous-variable semi-device-independent QRNGs."],"fun_headline_variants":["Four-state coherent states certify 0.223 bits per heterodyne measurement","Semi-device-independent QRNG certifies 0.223 bits with integrated heterodyne receiver","Four-state constellation certifies 0.223 bits per measurement","Energy-constrained QRNG with integrated receiver certifies 0.223 bits"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The photon-number constraints on the source states are sufficient, when combined with semidefinite relaxation techniques, to compute tight lower bounds on the certifiable Shannon entropy.","fun_headline_variants_meta":{"raw":{"variants":["Four-state coherent states certify 0.223 bits per heterodyne measurement","Semi-device-independent QRNG certifies 0.223 bits with integrated heterodyne receiver","Four-state constellation certifies 0.223 bits per measurement","Energy-constrained QRNG with integrated receiver certifies 0.223 bits"]},"model":"grok-4.3","cost_usd":0.010965,"raw_usage":{"total_tokens":4811,"prompt_tokens":635,"num_sources_used":0,"completion_tokens":79,"cost_in_usd_ticks":109649500,"prompt_tokens_details":{"text_tokens":635,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":4097,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":635,"tokens_out":79,"duration_ms":25044,"temperature":1.0,"reasoning_tokens":4097,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T08:03:48.052639+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An experiment that records the heterodyne statistics of the four-state constellation while enforcing the stated photon-number bound and finds that the resulting semidefinite program returns an entropy lower bound materially below 0.223 bits per measurement.","supporting_citations":[],"review_version":1}