{"id":"374638f2-150d-4506-8176-fafcc31df880","arxiv_id":"2608.09364","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"Closed-form estimators recover per-link loss, success, and co/counter-propagation depolarization in quantum-classical coexistence networks from end-to-end measurements, with identifiability fixed by flipping one classical signal direction.","lead":"This paper presents a tomography framework for quantum-classical coexistence networks, where quantum and classical signals share optical fiber, that estimates each link's loss, success, and direction-dependent depolarization from end-to-end photon-count measurements.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Network estimators rely on a multiplicative Raman-injection convention that Remark 5 concedes is non-physical; the missing two-link physical test is the load-bearing gap.","rationale":"The reader's weakest assumption is exactly the injection convention, and I agree it is the most load-bearing point: the paper's genuinely new network contribution (star gauge argument, tree peeling, mesh least-squares) all consume Proposition 4, so if the multiplicative composition law is not physical, the network-level estimators are not recovering the advertised per-link parameters. The paper is transparent about this in Remark 5 and in the proposed two-link experiment, which is why this reads as a conditional gap rather than an internal algebra error. A secondary concern is the construction of M in \\S VI-A via M=R(1-p/2), which risks making the QLT-versus-BPT comparison circular; that would weaken the single-link experimental validation but not the algebraic core. Since the reader already assigned a conditional verdict on essentially this basis, my read does not move the verdict.","tokens_in":30597,"tokens_out":9719,"duration_ms":102214,"concrete_test":"Splice two calibrated spools (e.g., 5 km and 15 km) with per-link (s, d^{(0)}, d^{(1)}, d^{(2)}) known from single-link QLT/BPT, then measure end-to-end R/T and M/T for both classical directions. Compare the data to (i) the multiplicative prediction \\prod r_e of Eq. (24) and (ii) the additive prediction t_2 r_1 + \\nu_2 of Remark 5, using per-link t_e=s_e+d_e^{(0)} and \\nu_e=d_e-d_e^{(0)} measured in isolation. If (ii) fits and (i) does not, Proposition 4 is empirically falsified and the star/peeling/least-squares estimators are biased; if (i) fits, the concern is settled.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Proposition 4's composition rule R_P/T_P = \\prod_{e\\in P}(s_e+d_e^{(x_e)}) (Eq. 24) is derived under the convention that Raman injection on each link scales with the photon population arriving at that link (\\nu_j R(j-1) in recursion (27)). Physically, spontaneous Raman is pumped by the classical signal alone and is attenuated only downstream; Remark 5 itself gives the physical formula R_P/T_P = \\prod_j t_j + \\sum_j \\nu_j \\prod_{k>j} t_k, with t_j=s_j+d_j^{(0)}, which agrees with (24) only when one link dominates injection or per-hop transmittances approach unity. In the measured coexistence regime (Table I: s\\approx 10^{-3}, d\\approx 0.03--0.6), per-hop transmittances are not near unity, so for a deployed two-hop path the multiplicative law is misspecified. Consequently the star estimators (21) and the peeling/least-squares estimators of \\S V-A invert an abstract multiplicative model rather than the physical per-link parameters; the gauge-flip of Lemma 3 fixes only a degeneracy inside that model and cannot correct the composition bias. The network-level central claim therefore depends on an acknowledged convention that has never been tested on a physical multi-link path.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a tomography framework for quantum-classical coexistence networks (QCNs), in which quantum and classical signals share fiber. It models each coexisting fiber via photon loss, successful transmission, and three direction-dependent depolarization ratios, and derives closed-form estimators for these parameters from end-to-end counts (Section IV). It then extends the approach to star networks using multiplicative path equations, resolving a residual gauge degeneracy by reversing the classical-signal direction on one link (Section V, Lemma 3), and further to trees and meshes via peeling and least-squares methods. Validation consists of single-link experimental data, emulated star networks composed from measured single-link channels, and synthetic Monte-Carlo simulations for general topologies.","tokens_in":30898,"tokens_out":5757,"duration_ms":55869,"significance":"If the central claims hold, the framework would be a useful tool for characterizing coexistence links without per-link access, and the star-network identifiability analysis with the single-link flip protocol is a genuine contribution. The algebraic derivations are self-consistent, the sample-complexity scaling law in Section VI-D is concrete and falsifiable, and the authors are candid about the limits of their validation, explicitly flagging the injection convention in Remark 5 and the missing physical two-link test. The significance of the network-level claim is, however, conditional on a physical multi-link composition test, since the multiplicative path rule is an acknowledged modeling convention rather than a demonstrated property of deployed fibers.","major_comments":[{"comment":"The matched-outcome count M is not an independent measurement: the text states that M is obtained from the aggregated counts together with the estimated depolarization probability via M=R(1-p/2), which is exactly the model identity E[M/T]=s+d(x)/2=r(x)(1-p(x)/2). Because the QLT estimators (16) invert this same identity, the QLT-versus-BPT agreement in Figs. 5–6 is circular for the depolarization parameters unless p is obtained from an independent procedure. The manuscript should either reconstruct M directly from per-basis matched-outcome counts without using p, or estimate p from an independent data split, and should then report how the agreement changes.","section":"§VI-A"},{"comment":"Equation (24) is derived from the recursion (27) in which Raman injection on each link scales with the incoming photon population (the ν_j R(j-1) term). Remark 5 acknowledges that physical spontaneous Raman is pumped by the classical signal alone and is attenuated only downstream, giving R_P/T_P = ∏_j t_j + ∑_j ν_j ∏_{k>j} t_k, and that the two formulas coincide only when one link dominates injection or per-hop transmittances approach unity. In the measured coexistence regime (Table I: s≈1e-3, d in 0.03–0.6) transmittances are not near unity, so on a deployed multi-hop path Eq. (24) is misspecified and the star estimators (21), the peeling estimator (30), and the least-squares solver (31) invert an abstract multiplicative model rather than the physical per-link parameters. The gauge flip of Lemma 3 fixes a degeneracy inside that model only and cannot remove this composition bias. This is the load-bearing gap: the central network-level claim requires a direct physical two-link test of (18)–(19), which is not provided.","section":"§V-A, Proposition 4 and Remark 5"},{"comment":"The multi-link validation is emulated by composing single-link channels with exactly the binomial cascade implied by the model under test (Type I), and Type II retains the same received-count model for R while only the matched fraction uses the BPT maps. Figure 10 shows a persistent bias on the 5-km link (s_2≈0.06 against truth 0.0015, with the depolarization estimates displaced by the same amount), which the authors attribute to model mismatch. Consequently the emulations do not establish that physical concatenated links obey (24); they only verify algebraic self-consistency of the estimators under the assumption that the multiplicative law holds. The conclusion lists a direct two-link experiment as future work, but this experiment is necessary to support the paper's central claim rather than optional.","section":"§VI-C"}],"minor_comments":[{"comment":"The displayed ordering of the six unknowns and the null vector v=(+1,-1,-1,+1,-1,+1) are inconsistent with the statement that v assigns +1 to every end-to-hub received ratio and −1 to every hub-to-end ratio; please align the ordering.","section":"§V, Lemma 3 proof"},{"comment":"The symbol T denotes both the launched-photon count in Section II and the tree (calligraphic T) in Section V-A; although calligraphic T avoids a collision, the notation remains easy to confuse and a rename would improve readability.","section":"§II and §V-A"},{"comment":"The code and data availability section states that the code will be made available upon publication; for a paper whose numerical claims rest on a custom Monte-Carlo sampler, an archival version should be deposited with the submission.","section":"Data and Code Availability"},{"comment":"The 'small residual gap' between Coex QLT and Coex BPT is not quantified; reporting the maximum or median fidelity gap across the eight wavelengths and three fiber lengths would strengthen the claim.","section":"§VI-B, Fig. 6"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a serious methods paper with honest limitations, but the two load-bearing issues—the circular construction of M and the unvalidated multiplicative injection convention—prevent acceptance in current form. The paper's literature coverage and acknowledgments are appropriate; the main editorial concern is that the network-level validation is emulative rather than physical, and the stated future work of a direct two-link test is in fact essential to the paper's central claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper has a genuinely useful single-link model and a clever gauge-fixing protocol, but the network-level claims rest on an acknowledged non-physical composition rule, and the single-link experimental comparison is partly circular. Keep the link tomography, be skeptical of the star and general-topology results until a physical two-link test exists.\n\nWhat's new: the direction-dependent depolarization model with three d(x), closed-form unbiased estimators in Eq. (16), the CPTP tensor-product formulation in §III that recovers the same observables, and the star-network gauge degeneracy with the single classical-direction flip to resolve it. The algebra is self-consistent, and the link estimators are √T-consistent with closed-form variances. That is real, reusable work.\n\nWhere it gets soft. First, the experimental validation of the link estimators is not independent. In §VI-A, M is obtained from the aggregated counts via M = R(1-p/2) using an estimated depolarization probability—exactly the model identity E[M/T]=s+d/2. So both Coex QLT and the BPT baseline consume an M that already assumes the depolarizing model; the agreement in Figs. 5–6 is partly baked in. The authors should derive M directly from the raw matched-outcome table and report any p used in its construction separately from the QLT estimate.\n\nSecond, the network-level composition rule of Proposition 4 assumes Raman injection on each link scales with the photon population arriving at that link. Remark 5 concedes the physical SpRS is pumped by the classical signal alone and attenuated only downstream, giving a different formula unless one link dominates or per-hop transmittances are near unity. In the measured regime (Table I, s~10^-3, d up to 0.6), transmittances are far from unity. So the star estimators in §V and the peeling/least-squares extensions in §V-A invert an abstract multiplicative model, not the physical per-link parameters; the gauge flip fixes only a degeneracy inside that model. The emulation and Monte-Carlo studies are self-consistent by construction—they compose the same model the estimators invert—so they cannot validate the composition law. The paper is honest about the missing multi-link testbed and even names the two-link physical test as the highest-value next experiment, but that means the central network-level claim is currently unvalidated.\n\nWho this is for: anyone doing quantum network tomography or coexistence QKD. The single-link model and the gauge argument are worth citing; the network results need revision. I would send it to a serious referee, but the referee should demand the raw-count M and either a physical justification of the injection convention or a bounded-bias analysis.","headline":"A clean closed-form link tomography result and a genuinely novel gauge-fixing protocol, but the network-level claims rest on a multiplicative Raman composition rule the authors themselves concede is non-physical, and the single-link validation is partly circular; the paper deserves a serious referee but the multi-link claims are not yet established.","tokens_in":31417,"tokens_out":2967,"would_cite":true,"duration_ms":27844,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P45","81P50"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper establishes that all per-link channel parameters of a coexisting fiber—success ratio, loss ratio, and three direction-dependent depolarization ratios—are recoverable in closed form from end-to-end photon counts, and that a…","keywords":["quantum-classical coexistence","network tomography","closed-form channel estimation","direction-dependent depolarization","Raman scattering","star network tomography","identifiability","quantum channel model"],"falsifier":"Splice two calibrated coexisting fiber spools, measure each single-link received ratio $r_i = R_i/T_i$ under identical classical traffic, then send a known input population through both and compare the measured end-to-end $R/T$ with the product $r_1 r_2$. If the product systematically disagrees while the downstream-attenuated formula of Remark 5 fits, the multiplicative composition rule that carries the network estimators is falsified.","tokens_in":30352,"feed_emoji":"⚛️","tokens_out":11055,"duration_ms":97808,"temperature":0.7,"pith_summary":"The paper tries to establish that a fiber carrying both quantum and classical signals can be fully characterized from end-to-end photon counts, without touching each link. Its channel model splits every input photon into three outcomes—loss, intact success, or depolarization—with the depolarization ratio depending on whether the classical signal is absent, co-propagating, or counter-propagating. The paper derives closed-form estimators for all five per-link parameters on a single fiber, and proves that in a star network the only remaining degeneracy is removed by flipping the classical-signal direction on one link. On experimental testbed data the link estimators track a full process-tomography baseline, so a sympathetic reader would take the framework as a candidate for practical quantum-network monitoring.","feed_headline":"One classical-signal flip recovers all per-link fiber parameters","feed_subtitle":"Closed-form estimators read per-link noise from end-to-end photon counts, matching full process tomography.","key_machinery":"The workhorse is a three-outcome population model: each input photon is either lost (ratio $q$), transmitted with polarization intact (ratio $s$), or depolarized (ratio $d^{(x)}$), with Raman-injected photons making the received ratio $r^{(x)} = s + d^{(x)}$ a per-photon yield that can exceed the loss-limited baseline. From this model the identity $\\mathbb{E}[M/T] = s + d^{(x)}/2$ gives the closed-form link estimators, and a recursion on intact versus depolarized populations gives the path-composition rule $R_P/T_P = \\prod_{e\\in P}(s_e + d_e^{(x_e)})$ together with $(2M_P - R_P)/T_P = \\prod_{e\\in P} s_e$. The star-network identifiability rests on Lemma 3: the six end-to-end received-ratio equations have rank five with a one-dimensional kernel, so a single flipped-link measurement appends a row with nonzero projection on that kernel and fixes the gauge under the flip-invariance assumption that reversing the classical direction interchanges co- and counter-propagation without introducing new unknowns.","core_discovery":"The central claim is that the coexisting fiber is characterized by the success ratio $s$, the loss ratio $q$, and the direction-dependent depolarization ratios $d^{(0)}$, $d^{(1)}$, $d^{(2)}$, and that these are identifiable from the two expected observables $\\mathbb{E}[R/T] = s + d^{(x)} = r^{(x)}$ and $\\mathbb{E}[M/T] = s + d^{(x)}/2$. The single-link estimators are closed form: $\\hat{d}^{(x)} = 2(R^{(x)} - M^{(x)})/T^{(x)}$ for each coexistence scenario and $\\hat{s} = \\frac{1}{3}\\sum_{x=0}^{2}(2M^{(x)} - R^{(x)})/T^{(x)}$, with $\\hat{q} = 1 - \\hat{s} - \\hat{d}^{(0)}$. Along a path the intact-photon count multiplies, $(2M_P - R_P)/T_P = \\prod_{e\\in P} s_e$, and the received ratio multiplies as $R_P/T_P = \\prod_{e\\in P}(s_e + d_e^{(x_e)})$, which is what lets star-network success ratios be extracted from pairwise end-node probes. The paper's key identifiability result is that the six received-ratio equations for a three-link star have rank five, with the kernel spanned by the vector that assigns $+1$ to each link's end-to-hub received ratio and $-1$ to each link's hub-to-end received ratio; reversing the classical-signal direction on a single link adds a measured equation that fixes this gauge and identifies all six direction-dependent depolarization ratios.","pith_inferences":["A decisive next step the paper itself proposes—splicing two calibrated spools and checking the multiplicative law against the downstream-attenuated formula of Remark 5—would settle whether the injection convention holds in practice.","The single-flip gauge-fixing trick could transfer to other direction-dependent noise mechanisms, such as polarization-mode dispersion or cross-phase modulation, wherever per-link unknowns pair by propagation direction.","If the multiplicative law survives in deployed fibers, regularized or non-negativity-constrained estimators with adaptive probe allocation could attack the super-exponential sample-size bottleneck, which the paper lists as an open direction."],"forward_implications":["Single-link tomography recovers depolarization probabilities and process fidelities that closely track the process-tomography baseline across fiber lengths and wavelengths, with the residual gap attributed to the depolarization-only model approximation.","Star networks can be fully characterized from edge measurements: per-link success ratios come from $\\hat{s}_k = \\sqrt{Q_{k,\\ell}Q_{k,m}/Q_{\\ell,m}}$, and the single-link classical-flip protocol resolves the remaining direction-dependent depolarization ratios.","Tree and mesh topologies inherit the same multiplicative observables: peeling gives per-link estimates on trees, and log-linear least squares with a full-column-rank path-by-link incidence matrix gives them on general graphs.","Network-level success-ratio estimation is expensive: the required sample size grows super-exponentially with path depth, following $T_{\\rm req}(n) = [s^n(1-s^n) + ((s+d)^n - s^n)]/(n^2 s^{2n} \\epsilon^2)$.","Operationally, the findings favor co-propagating classical traffic, shallow monitored paths, and placing quantum wavelengths away from the classical carrier line."],"supporting_citations":[{"why":"Supplies the experimental testbed dataset, the process-tomography baseline, and the per-wavelength depolarization measurements used to validate the link estimators.","marker":"[32]"},{"why":"Establishes the direction-dependent Raman-noise mechanism and scaling that motivates the co- and counter-propagation depolarization structure and the power-preservation condition for the flip.","marker":"[13]"},{"why":"Provides the classical multicast loss-tomography estimator whose multiplicative form the success-ratio estimator inherits.","marker":"[22]"},{"why":"Contributes the progressive-etching peeling schedule reused for tree topologies.","marker":"[12]"},{"why":"Supplies the network-tomography identifiability framework formalized in Proposition 6.","marker":"[7]"},{"why":"Provides the Raman-amplifier model used for the first-order accumulation integrals in the physical interpretation of $d^{(x)}$.","marker":"[29]"},{"why":"Supports the coherent Raman-noise mode structure and the weak-injection assumption behind the two-mode channel factorization.","marker":"[30]"}],"fun_headline_variants":["One flip, all per-link fiber parameters from photon counts","Closed-form tomography: per-link noise from end probes alone","Direction flip resolves quantum-classical fiber noise","Photon counts alone yield per-link channel parameters","Matches full process tomography with closed-form estimators"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that per-link received ratios multiply along a path, the injection convention of Proposition 4; if deployed Raman injection is pumped by the classical signal alone and is only attenuated downstream, as Remark 5 notes, then the network-level estimators are biased even when the single-link model is correct.","fun_headline_variants_meta":{"raw":{"variants":["One flip, all per-link fiber parameters from photon counts","Closed-form tomography: per-link noise from end probes alone","Direction flip resolves quantum-classical fiber noise","Photon counts alone yield per-link channel parameters","Matches full process tomography with closed-form estimators"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001274,"raw_usage":{"total_tokens":5338,"prompt_tokens":1202,"completion_tokens":4136,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":818,"completion_tokens_details":{"reasoning_tokens":4063}},"tokens_in":818,"tokens_out":4136,"duration_ms":22454,"temperature":1.0,"reasoning_tokens":4063,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T18:42:02.989191+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Splice two calibrated coexisting fiber spools, measure each single-link received ratio $r_i = R_i/T_i$ under identical classical traffic, then send a known input population through both and compare the measured end-to-end $R/T$ with the product $r_1 r_2$. If the product systematically disagrees while the downstream-attenuated formula of Remark 5 fits, the multiplicative composition rule that carries the network estimators is falsified.","supporting_citations":[{"cited_title":"Coexistent quantum channel characterization using spectrally resolved bayesian quantum process tomography,","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental testbed dataset, the process-tomography baseline, and the per-wavelength depolarization measurements used to validate the link estimators."},{"cited_title":"Multicast- based inference of network-internal loss characteristics,","cited_arxiv_id":null,"evidence_quote":"Provides the classical multicast loss-tomography estimator whose multiplicative form the success-ratio estimator inherits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the network-tomography identifiability framework formalized in Proposition 6."},{"cited_title":"Raman amplifier model in single- mode optical fiber,","cited_arxiv_id":null,"evidence_quote":"Provides the Raman-amplifier model used for the first-order accumulation integrals in the physical interpretation of $d^{(x)}$."},{"cited_title":"Dense wavelength multiplexing of 1550 nm qkd with strong classical channels in reconfigurable networking environments,","cited_arxiv_id":null,"evidence_quote":"Supports the coherent Raman-noise mode structure and the weak-injection assumption behind the two-mode channel factorization."}],"review_version":1}