{"id":"ec660982-309e-4e23-996a-99cec7d7c94c","arxiv_id":"2608.01723","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Jointly optimizing ring radius ratios, ring probabilities, and modulation variance extends the modeled maximum transmission distance of 16-APSK discrete-modulated CV-QKD by about 15% over conventional binomial APSK.","lead":"By tuning the ring radii, ring probabilities, and signal strength of an M-APSK light pattern, this paper extends the modeled transmission distance of discrete-modulated CV-QKD by about 15% for the 16-point case. The result is an optimization study inside an existing security model, a step toward simpler transmitters that reach further in quantum key distribution.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 15% distance gain rests on the tightness of the Z* bound from [15] for optimized constellations; the paper explicitly bypasses newer composable security analyses [26-29], so the improvement may be an artifact of the security model.","rationale":"After reading the paper carefully, I find that the most load-bearing assumption is the validity of the security model for ranking constellations. The reader's weakest_assumption identifies exactly this, and I agree. The paper is an optimization study within an inherited model; the headline 15% improvement is the value of the model's objective at its optimum. If the model's bound is not equally tight for all constellations, the ranking can be distorted, and the improvement may not be genuine. The paper itself flags the existence of newer security analyses but does not engage with them, which is a clear limitation. I do not see an internal inconsistency that would invalidate the optimization; the Gram-matrix method and the optimization procedure are logical. The grid-resolution inconsistency between §4.1 and Table 2 is concerning but does not overturn the qualitative gain; it does suggest that the exact numbers are sensitive to grid choices. However, the security-model concern is more severe: it questions whether the gain exists at all outside the specific bound. Therefore, the verdict should remain CONDITIONAL, contingent on validating the optimized constellations against at least one of the newer composable security analyses. My proposed test does exactly that: recompute the key rates using the composable finite-size security proof of Ref. [28]. If the improvement persists, the central claim is supported; if not, it is an artifact. Since the reader already set CONDITIONAL and my analysis does not move the verdict, I set verdict_should_be to UNCHANGED.","tokens_in":974,"tokens_out":997,"duration_ms":132535,"concrete_test":"Recompute the finite-size secret key rate for the conventional binomial 16-APSK (r=[0.50,1], p=[0.75,0.25], V_A=1.20) and the proposed r,p-optimized 16-APSK (r=[0.41,1], p=[0.71,0.29], V_A=1.30) from Table 1, using the composable finite-size security analysis of Kanitschar et al. [28] (PRX Quantum 4, 040306, 2023) for discrete-modulated CV-QKD, under the same channel and detector parameters as in the paper. If the optimized constellation does not yield a longer maximum transmission distance than the conventional binomial at K_th=1e-5 bits/use, the 15% gain claimed via Z* is an artifact of the [15] bound.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that optimizing ring radii and probabilities increases the maximum transmission distance of 16-APSK by ~15% in the finite-size secret key rate model. This claim depends on Eq. (1), which uses the Z* lower bound of Eq. (2) from [15] and parameters inherited from [17]. The paper explicitly states in §2.1 that it does not use the newer composable security analyses [26-29]. Since Z* is a lower bound, the computed key rate is only as meaningful as the bound's tightness. If the bound is looser for the optimized constellation than for the conventional binomial constellation, the key rate of the optimized structure is artificially inflated, and the 15% gain could be a numerical artifact. The paper provides no evidence that the tightness of the bound is similar across the compared structures, nor does it compare against the finite-size security proofs of Refs. [26-29] that could validate the ranking. The reported inconsistency between fine-grid (46.39 km, 14.49%) and coarse-grid (46.6 km, 15.06%) 16-APSK results is a secondary symptom that the numerical optimization is not fully robust, but the security-model issue is primary: without validation of the bound's uniformity, the central claim's external validity is unestablished.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a numerical optimization of ring radius ratios and ring probabilities for multi-ring M-APSK constellations in discrete-modulated continuous-variable QKD, using a Gram-matrix spectral decomposition of the average state to compute the Z* correlation parameter in the finite-size secret key rate model of Ref. [17]. The joint search over (V_A, r, p) is reported to extend the maximum transmission distance at K_th = 1e-5 bits/use by about 15% for 16-APSK (46.6 km vs 40.5 km), with smaller gains of 10.93% for 32-APSK and 6.94% for 64-APSK. The fidelity between the discrete average state and the Gaussian thermal state is used as a structural diagnostic.","tokens_in":12119,"tokens_out":5010,"duration_ms":56809,"significance":"The Gram-matrix method in Sec. 2.3 is correct and standard, and the fidelity formula in Eq. (25) is appropriate. The internal comparison is fair: the baseline and proposed constellations are evaluated with the same security model and simulation parameters. If the ranking is robust across security models, the paper offers a simple, practical constellation-shaping technique (two scalar parameters per ring) for DM-CV-QKD, with a clear and physically sensible trend that gains shrink as the constellation approaches the Gaussian average state. However, the central 15% claim rests on the inherited lower-bound security model from Ref. [15]; the paper does not validate the tightness of this bound for the optimized constellations, which is the main correctness risk.","major_comments":[{"comment":"The distance-gain claim is computed with the Z* lower bound of Ref. [15] in the finite-size model of Ref. [17]. Since Z* is a lower bound, the key-rate comparison is meaningful only if the bound's slack is approximately uniform for the conventional and r,p-optimized constellations. The paper provides no tightness check and explicitly bypasses the composable security analyses [26–29]. If the bound is looser for the optimized structures, the reported gain could be an artifact. Please validate the ranking for at least one optimized constellation (e.g., 16-APSK) against the finite-size security proof of Ref. [28] or [29], or provide an independent estimate of the bound's slack.","section":"§2.1, Eq. (2); §4.1, Table 2"},{"comment":"The improvement direction is guaranteed by construction: the conventional binomial constellation is a feasible point in the joint (V_A, r, p) grid, so the optimum of Eq. (20) cannot be lower than the conventional rate. The paper should state this explicitly and frame the result as the magnitude of the achievable gain rather than as evidence that the optimized structure is intrinsically superior. This is important for calibrating the reader's expectations, though it does not invalidate the optimized parameters.","section":"§3.1, Eq. (20)"}],"minor_comments":[{"comment":"The operator τ^{-1/2} is not defined for low-rank τ. Please state explicitly that the inverse is taken on the support of τ (pseudo-inverse), consistent with the later description in Sec. 2.3.","section":"§2.2, Eq. (2)"},{"comment":"In Eq. (14), if some λ_j are zero the expression is undefined. Clarify that the spectral decomposition and the eigenvectors are restricted to the nonzero eigenvalues.","section":"§2.3, Eq. (14)"},{"comment":"The fine-grid result in §4.1 gives 46.39 km and 14.49% improvement, while Table 2 reports 46.6 km and 15.06% using a coarser distance step. The discrepancy is likely due to the 0.1-km distance grid in §4.2; the fine-grid number should be the headline, and the grid-resolution sensitivity should be reported.","section":"§4.1 and Table 2"},{"comment":"Figure 3 and 5 are difficult to read in the text: the curves are not labeled in the caption, and the reference Gaussian state should be specified with the same V_A as the discrete states. Please add clear legends and ensure the figures are legible in print.","section":"Figs. 3 and 5"},{"comment":"The V_A values in Table 1 are stated at the maximum-distance threshold, but the exact operating point (e.g., optimum at the threshold crossing) should be defined. Also clarify whether these are the grid-search values with the given steps.","section":"§4.2, Table 1"},{"comment":"There are several typographical and grammatical issues: 'a t' in the Fig. 4 caption, inconsistent hyphenation of 'multi-ring', missing articles, and Ref. [20] lists an arXiv number with year 2026; please verify the reference.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper is a modest but potentially useful extension of Ref. [17], and the internal optimization is correctly executed. The main risk is that the security model's lower bound may not rank constellations accurately; this is not a fatal flaw but requires additional validation. If the authors can demonstrate the ranking persists under a composable security proof for at least one optimized constellation, the paper would be publishable. The fine/coarse grid discrepancy also weakens the precision of the headline claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does exactly what it says: it treats ring radii and ring probabilities as tunable variables for M-APSK constellations in discrete-modulated CV-QKD, and optimizes them under the finite-size key-rate model of [17] using the Z* lower bound from [15]. The Gram-matrix spectral method is correct and standard, the fidelity analysis is a nice structural diagnostic, and the comparison against the conventional binomial constellation is fair. The result—roughly 15% distance extension for 16-APSK, shrinking to 7% for 64-APSK—is a genuine in-model improvement, and the authors are upfront that they are not proposing a new security proof.\n\nThe main soft spot is the one the stress-test flags: the computed key rate is only as good as the Z* bound's tightness for the optimized constellations. The paper never checks whether that bound is equally tight for the optimized states as for the conventional ones, and it explicitly bypasses the newer composable analyses [26–29]. So the 15% gain could, in principle, be a numerical artifact of a looser bound. That said, the paper is transparent about this scope: it uses the same model as the baseline precisely to isolate the constellation effect. It's a limitation, not a hidden flaw, and a serious referee should ask the authors to discuss or at least sanity-check bound tightness for their optimized states.\n\nTwo smaller issues: the grid-search inconsistency (46.39 km fine-grid vs 46.6 km coarse-grid) is odd and slightly undermines confidence in numerical robustness, though it's plausibly due to the different step sizes in V_A and L. Also, no code or data is shipped, and the inherited parameters from [17] are not listed, making independent replication needlessly difficult.\n\nThis is a competent, narrowly scoped engineering paper. It deserves a serious referee, not a desk reject, but the referee should push for a bound-tightness check or a clear statement that the improvement is model-relative. I'd route it to someone who works on DM-CV-QKD security proofs, not just constellation shaping.","headline":"A clean, transparent in-model optimization study for M-APSK constellations in DM-CV-QKD; the ~15% distance gain is real within the chosen security model, but its external validity rests on an unchecked bound-tightness assumption.","tokens_in":12771,"tokens_out":2750,"would_cite":false,"duration_ms":32779,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P94"],"pacs":["03.67.Dd"],"model":"deepseek-v4-flash","headline":"Optimizing ring radii and probabilities extends 16-APSK CV-QKD reach by about 15 percent.","keywords":["continuous-variable quantum key distribution","discrete modulation","M-APSK constellation","constellation shaping","finite-size secret key rate","Gram matrix","fidelity"],"falsifier":"Recompute the threshold distance for the r,p-optimized 16-APSK constellation (r = [0.41,1], p = [0.71,0.29], V_A = 1.30) using a composable finite-size security proof such as those cited as [28] or [29], and compare it against the conventional binomial constellation; if the optimized constellation no longer beats the binomial, the 15% gain is an artifact of the [15] bound.","tokens_in":11646,"feed_emoji":"🔐","tokens_out":4934,"duration_ms":51249,"temperature":0.7,"pith_summary":"This paper argues that the fixed ring spacings and fixed selection probabilities used in conventional multi-ring APSK modulation for discrete-modulated CV-QKD are not optimal. By treating ring radius ratio, ring probability, and modulation variance as joint optimization variables under a fixed finite-size secret key rate model, the authors find constellations whose average state sits closer to the ideal Gaussian thermal state, raising the correlation parameter Z* that enters the security bound. The concrete payoff is reach: at the 1e-5 bits/use threshold, 16-APSK (4+12) extends from about 40.5 km to 46.6 km, a roughly 15% gain, with smaller gains of about 10.9% and 6.9% for 32- and 64-APSK. The gain shrinks as constellation size grows because larger APSK sets already approximate Gaussian modulation. If the paper is right, simple geometric and probabilistic shaping of existing APSK formats can buy a real distance extension without changing the protocol, detector, or channel model.","feed_headline":"16-APSK ring optimization extends CV-QKD reach by 15 percent","feed_subtitle":"Jointly tuning ring radii and probabilities beats fixed binomial shaping; smaller constellations gain most.","key_machinery":"The Gram matrix G = V†V built from weighted coherent states, whose nonzero eigenvalues coincide with those of the average state τ = VV†, supplies the spectral decomposition needed to evaluate the fractional powers τ^{1/2} and τ^{-1/2} appearing in the correlation bound Z* from [15]. A grid search over (V_A, r, p) then maximizes the finite-size key rate at each distance, and the fidelity F(τ_D, τ_G) between the discrete average state and the Gaussian thermal state acts as a structural diagnostic connecting the geometric change to the key-rate gain.","core_discovery":"For each transmission distance, the paper jointly searches the modulation variance V_A, ring radius ratio r, and ring probability p to maximize the finite-size secret key rate, using the same rate model and channel parameters as the conventional multi-ring M-APSK baseline [17]. The optimized 16-APSK (4+12) constellation—inner ring radius ratio pulled inward from 0.50 to 0.41 and outer-ring probability raised from 0.25 to 0.29—increases the threshold distance at K = 1e-5 bits/use from 40.5 km to 46.6 km. The average state of the optimized constellation has higher fidelity to the Gaussian thermal state and a higher Z* value, and the paper uses this as evidence that the gain is structural: the","pith_inferences":["Because the result relies on the [15] lower bound with fixed reconciliation efficiency, the 15% gain is an in-model result; under the newer composable finite-size security analyses cited in the paper ([26]–[29]), the relative gain could shrink, grow, or reverse. Testing the optimized constellation under those proofs is a natural next step.","Fidelity to the Gaussian thermal state may serve as a fast pre-screening proxy for constellation search, since it separated structures more cleanly than Z* in the paper's figures; however, the paper does not prove a monotone link, so this should be validated before relying on it.","The same r,p-optimization recipe could be applied to other multi-amplitude formats such as probabilistically shaped QAM or 128-APSK under the same model; the expected gain should scale with their distance from Gaussian modulation.","The optimized constellations change only transmitted amplitudes and probabilities, so the predicted 16-APSK threshold of 46.6 km is a concrete, testable prediction for an experimental implementation with existing APSK transmitters."],"forward_implications":["The binomial ring probability is not generally optimal: it happens to be close to a good probability shaping for 16-APSK, but for larger multi-ring APSK the optimized probabilities differ more markedly.","Smaller constellations have the most to gain from radius-probability optimization, because their average state has a larger structural gap from Gaussian modulation.","The Gram matrix method reduces the eigen decomposition from a large truncated Fock-space matrix to an M×M Gram matrix, making joint constellation optimization feasible for multi-ring APSK.","The optimized patterns—inner rings shifted inward and ring probabilities more evenly distributed—suggest a practical design rule for APSK modulation in discrete-modulated CV-QKD."],"supporting_citations":[{"why":"Supplies the baseline multi-ring M-APSK structure, its uniform and binomial ring probabilities, and the finite-size rate model and channel parameters that the optimization inherits.","marker":"[17]"},{"why":"Provides the explicit Z* lower bound on Alice–Bob correlation for arbitrary modulation, which is the quantity the optimized average state must raise.","marker":"[15]"},{"why":"Gives the finite-size secret key rate formula (together with [17]) whose threshold defines the transmission-distance comparisons.","marker":"[25]"},{"why":"Defines the quantum fidelity used as the structural diagnostic comparing discrete and Gaussian average states.","marker":"[30]"},{"why":"Gives the Gaussian thermal-state description used as the reference average state for fidelity calculations.","marker":"[6]"}],"fun_headline_variants":["Tuning ring radii and odds boosts CV-QKD range by 15%","Joint ring shaping extends discrete-modulated CV-QKD by 15%","Optimized APSK rings push CV-QKD distance 15% farther","CV-QKD reach +15% via optimized M-APSK rings"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The ranking of constellations by the inherited security model is taken as correct: the Z* lower bound from [15] is assumed to be equally tight for the optimized states, and reconciliation efficiency is fixed, so if the bound is looser for the new constellations the distance gain is an artifact of the model rather than a real improvement.","fun_headline_variants_meta":{"raw":{"variants":["Tuning ring radii and odds boosts CV-QKD range by 15%","Joint ring shaping extends discrete-modulated CV-QKD by 15%","Optimized APSK rings push CV-QKD distance 15% farther","CV-QKD reach +15% via optimized M-APSK rings"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000543,"raw_usage":{"total_tokens":2403,"prompt_tokens":676,"completion_tokens":1727,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":420,"completion_tokens_details":{"reasoning_tokens":1647}},"tokens_in":420,"tokens_out":1727,"duration_ms":14433,"temperature":1.0,"reasoning_tokens":1647,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T22:07:02.160580+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the threshold distance for the r,p-optimized 16-APSK constellation (r = [0.41,1], p = [0.71,0.29], V_A = 1.30) using a composable finite-size security proof such as those cited as [28] or [29], and compare it against the conventional binomial constellation; if the optimized constellation no longer beats the binomial, the 15% gain is an artifact of the [15] bound.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the baseline multi-ring M-APSK structure, its uniform and binomial ring probabilities, and the finite-size rate model and channel parameters that the optimization inherits."}],"review_version":1}