{"id":"4bd1f99d-ef02-4554-9358-0e857986577e","arxiv_id":"2607.25179","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Using teleportation-based demodulation, one optical mode can carry both QPSK classical data and distillable continuous-variable entanglement, with a sharp trade-off between classical bit-error rate and entanglement/key rate.","lead":"This paper shows how a single optical signal can carry both ordinary classical data and a quantum-entangled state at the same time, by using teleportation to read the data without destroying the entanglement. The goal is to let existing classical communication links double as entanglement distribution channels for future quantum networks.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"One-way protocol claim rests on reverse coherent information, a two-way/reverse-assisted bound; footnote 58 admits contradiction.","rationale":"The reader's weakest assumption is that RCI is used as a lower bound for distillable entanglement even though the protocol is one-way. I agree this is the most load-bearing concern because the paper's main quantitative claim — positive distillable entanglement — is supported only by R, which is not a valid lower bound for one-way LOCC. The footnote's explicit admission makes the gap concrete and in-scope. The Gaussian-extremality step, while also flagged by the reader, is backed by a published citation and is less clearly wrong; the one-way/RCI mismatch is self-acknowledged and directly affects whether the central claim is supported. The proposed forward coherent information check would settle the issue: a positive forward bound would validate the one-way claim, while a non-positive value would require the authors to either restrict the claim to two-way-assisted settings or present a different one-way bound. Since this is an addressable gap, the conditional verdict is appropriate and no change to the reader's verdict is recommended.","tokens_in":22268,"tokens_out":24624,"duration_ms":234696,"concrete_test":"Compute the forward coherent information I(A>B) = S(B) - S(AB) for the Gaussian state with covariance V_out from Eq. (38) at the same optimized parameters used in Fig. 3 (η = 30 dB, ε = 0.025, e_C = 10^-6 and 10^-7, optimized r_A and r_B). If I(A>B) ≤ 0 in the region where R > 0, the one-way distillability claim fails; if I(A>B) > 0, the concern is resolved for near-Gaussian output states and the paper should report this forward bound instead of relying solely on R.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The protocol as described is explicitly one-way: Alice transmits a displaced mode, Bob teleports and applies local feed-forward; no backward classical channel is used. The paper's central quantitative evidence for 'distillable entanglement' is the reverse coherent information R = S(A) - S(AB) of the output state. R is a valid lower bound for two-way or reverse-assisted entanglement distillation, but for one-way LOCC (the setting the protocol claims) the standard lower bound is the forward coherent information I(A>B) = S(B) - S(AB). The manuscript never reports I(A>B). Footnote 58 states: 'It may seem unreasonable to claim that Bob does not have a backwards communications channel, as we do in the body of the paper, and then quantify the distillable entanglement explicitly in terms of a reverse-assisted capacity. We are obliged to ignore this apparent contradiction.' This is not merely a framing issue: if the forward coherent information is non-positive in the regime where R > 0, then the claimed distribution of one-way distillable entanglement is not established by the presented results. The practical availability of two-way communication in deployments does not rescue the one-way claim as stated. A separate concern, Gaussian extremality for RCI, is cited and may be valid, but the one-way/RCI mismatch is self-admitted and directly affects the central conclusion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript theoretically analyzes a protocol that aims to transmit classical data and continuous-variable (CV) Gaussian entanglement simultaneously on a single optical mode. Alice prepares a two-mode squeezed vacuum, classically modulates one mode via QPSK displacements, and sends it through a lossy thermal channel. Bob performs a CV teleportation of the received mode using his own two-mode squeezed state; the dual-homodyne outcomes provide both the classical demodulation and the feedforward correction needed to approximate a zero-mean entangled state. The authors derive the bit-error rate, the ensemble covariance matrix of the output state, and lower bounds on reverse coherent information, entanglement of formation, and asymptotic secret-key rate. They conclude that positive reverse coherent information is achievable for sufficiently low classical bit-error rates, e.g. e_C ≤ ~5e-7 at 30 dB loss, and compare the scheme with the SQCC-QKD protocol of Ref. [27].","tokens_in":22561,"tokens_out":9289,"duration_ms":92175,"significance":"If the central claim is correct, the protocol is a conceptually useful step toward integrating classical communication with entanglement distribution in future quantum networks: existing classical links could, in principle, be augmented to distribute CV entanglement without sacrificing classical service. The analytic derivation of the output covariance matrix and the bit-error rate is detailed and, on its face, internally consistent; the paper also gives explicit formulas for RCI, E_F, and K∞ that can be checked by others. These are genuine strengths. However, the main quantitative evidence for \"distillable entanglement\" rests on an assumption about the operational meaning of the reverse coherent information that is explicitly acknowledged as contradictory in footnote 58, and the Gaussian-extremality step for RCI is asserted rather than proved. These issues directly affect the headline threshold numbers and must be resolved before the central claim is established.","major_comments":[{"comment":"The protocol is described as one-way: Alice transmits, Bob teleports and applies local feedforward, and no backward classical channel is used. Yet the distillable-entanglement claim is quantified by the reverse coherent information R = S(ρ_A) − S(ρ_AB), which is a lower bound on reverse-assisted or two-way entanglement distillation, not on one-way distillable entanglement. The manuscript never reports the forward coherent information I(A>B) = S(ρ_B) − S(ρ_AB), which would be the standard one-way lower bound. Footnote 58 openly acknowledges: \"It may seem unreasonable to claim that Bob does not have a backwards communications channel... We are obliged to ignore this apparent contradiction.\" This is not merely cosmetic: if R > 0 but I(A>B) ≤ 0 in the plotted regime, the stated one-way protocol does not distribute one-way distillable entanglement according to the presented evidence. Please e","section":"Section IV and Appendix B, Eq. (43)/(B1)–(B4); footnote 58"},{"comment":"The lower bound R_out ≥ S(ρ_G_A) − S(ρ_G_AB), where ρ_G is the Gaussian state with the same covariance matrix as the non-Gaussian ensemble output, is attributed to \"Gaussian extremality\" without proof or a specific theorem reference. The output is a mixture of Gaussian components with different displacement means, and replacing it by a single zero-mean Gaussian is nontrivial for the difference S(A) − S(AB): Gaussian states maximize the entropies S(A) and S(AB) separately for fixed covariance, but it is not automatic that the difference is minimized by the Gaussian state. If this extremality step fails, the RCI thresholds in Figs. 2(a) and 3 are not established. Please supply a proof or a precise citation for this particular use of Gaussian extremality.","section":"Appendix B, Eq. (B4)"}],"minor_comments":[{"comment":"The four branches of the conditional displacement are all labeled \"x0 ≥ 0, y0 ≥ 0\"; they should be the four sign combinations. This is clearly a typo, but it makes the appendix hard to follow.","section":"Appendix A, Eq. (A27)"},{"comment":"The relation between the single-symbol covariance matrix, which contains the term −||µ_B^{d1}||², and the full-alphabet covariance matrix, which does not, is implicit. A brief explanation that the full-alphabet covariance combines the average of the component covariances with the covariance of the component means would remove ambiguity.","section":"Eqs. (26)–(27) vs. (37)–(38)"},{"comment":"The protocol is called \"Gaussian CMQC\" although the output state is explicitly non-Gaussian and only approximated by a Gaussian state. A more precise term, such as \"Gaussian-approximated CMQC,\" would avoid confusion.","section":"Throughout"},{"comment":"The key-rate lower bound assumes Alice and Bob perform a heterodyne measurement on the output state, while the only measurement described in the protocol is Bob's dual-homodyne teleportation measurement. If additional measurements on the retained modes are intended for key generation, this should be stated explicitly and reconciled with the protocol timing.","section":"Section IV, key-rate calculation"},{"comment":"The color scale in the heat maps is not described adequately for the printed version; please add a clear caption describing the shading and the boundary line.","section":"Figure 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope and the protocol idea is interesting. The main issue is not the derivations themselves but whether the stated one-way protocol supports the claimed distillable-entanglement interpretation: the RCI mismatch is self-admitted and the Gaussian-extremality step is under-specified. Both issues are fixable by reframing the claims or adding the missing computation/proof, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: the paper has a good idea and solid-looking Gaussian analysis, but it leans on a reverse coherent information bound for a one-way protocol, and the authors themselves admit the mismatch in footnote 58. That is the thing to fix before the central claim stands.\n\nWhat's new: this applies the authors' earlier CMQC framework to entanglement distribution, with a concrete QPSK encoding, lossy thermal channel, teleportation-based demodulation, and a full covariance-matrix characterization of the output state. The bit-error-rate and the RCI/EOF/key-rate computations are detailed, and the asymptotic formulas agree between main text and appendices. Credit where earned: the derivation of V_out = [[a0 I, c0(1−δ)σZ],[c0(1−δ)σZ,(b0+Δ)I]] and the ε_MTEN and e_C thresholds is a genuine quantitative step beyond the existing SQCC literature, and the paper is transparent about its assumptions.\n\nThe soft spots. The load-bearing one is the RCI/one-way contradiction. RCI is a lower bound on distillable entanglement only for reverse-assisted or two-way scenarios. The protocol body describes a one-way feedforward scheme, with no backward channel. The paper never reports the forward coherent information I(A>B). If I(A>B) is non-positive where R is positive, then the claim of one-way 'distillable entanglement' is not supported. Footnote 58 says they 'are obliged to ignore this apparent contradiction' because practical implementations would have two-way communication. That is an honest admission, but it doesn't fix the inconsistency — either describe the protocol as two-way/reverse-assisted, or compute the forward bound, or soften the claim. This is addressable, but it is not cosmetic.\n\nSmaller issues: the Gaussian extremality step for the non-Gaussian mixture is cited rather than proven, which is fine if the citation is correct but worth a check. The discussion of repeater suitability and the 'alternative proof of security' comment outrun the actual derivations; those are forward-looking, not results. The protocol foundation is the authors' own unpublished preprint [1], which is available and not a problem by itself, but it does mean the current paper should be reviewed with an eye on that dependence.\n\nWho this is for: people working on CV quantum networking, hybrid classical-quantum links, and teleportation-based demodulation. It's a legitimate topic and the paper deserves a serious referee. My recommendation: send it to review, but make the RCI issue the first thing the referee is asked to resolve.","headline":"Good hybrid classical-quantum protocol analysis, but the RCI/one-way mismatch in footnote 58 needs to be resolved before the entanglement-distribution claim holds.","tokens_in":23021,"tokens_out":2828,"would_cite":false,"duration_ms":29603,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P45","81P47","94A40"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper shows that a single lossy optical mode can carry both classical bits and continuous-variable Gaussian entanglement, with positive distillable entanglement when classical errors stay below a loss-dependent threshold.","keywords":["continuous-variable quantum communication","simultaneous classical and quantum communication","entanglement distribution","quantum teleportation","Gaussian states","reverse coherent information","quantum key distribution","classically-modulated quantum communication"],"falsifier":"Compute or measure the one-way distillable entanglement of the output state for parameters where the paper's RCI bound is positive (e.g., η=30 dB loss, ε=0.025 SNU, e_C=10^-6); if the forward-only distillable entanglement is zero while the RCI lower bound is positive, the claim that the protocol distributes distillable entanglement under one-way communication is falsified. Alternatively, an experimental attempt to distill EPR entanglement from the output state under one-way classical communication at 30 dB loss with e_C=10^-6 would settle it.","tokens_in":22143,"feed_emoji":"🔗","tokens_out":5977,"duration_ms":48017,"temperature":0.7,"pith_summary":"The paper claims that a protocol called classically-modulated quantum communication (CMQC) can simultaneously transmit classical bits and continuous-variable (CV) entanglement over a single lossy optical channel. Bob receives Alice's displaced entangled mode and teleports it onto his own entangled mode; the teleportation measurement both decodes the classical signal and preserves the quantum correlations. After Bob applies a corrective displacement based on his estimated symbol, the shared state is a zero-mean non-Gaussian entangled state well approximated by a Gaussian with a known covariance matrix. The authors derive the classical bit-error rate and lower-bound the reverse coherent information, entanglement of formation, and secret-key rate, showing that distillable entanglement survives up to tens of decibels of loss when the classical error rate is below about 10^-6 to 10^-9. If correct, existing classical optical networks could be retrofitted to also distribute entanglement without sacrificing classical uptime.","feed_headline":"Teleportation packs data and entanglement onto one pulse","feed_subtitle":"A teleportation readout decodes the message and preserves the quantum state, keeping entanglement distillable.","key_machinery":"The key mechanism is the dual use of continuous-variable teleportation as a demodulator: Bob mixes Alice's received mode with his own EPR state, and the dual-homodyne measurement outcomes both teleport the quantum state (via displacement feed-forward) and estimate Alice's classical QPSK symbol. The load-bearing identity is the output covariance matrix V_out = [[a0 I, c0(1−δ)σZ], [c0(1−δ)σZ, (b0+Δ)I]] with Δ = 2α²τ e_C, which quantifies how classical bit errors convert into an effective excess-noise term on the entangled state. The paper then invokes Gaussian extremality to turn this Gaussian surrogate into lower bounds on RCI, entanglement of formation, and the Devetak-Winter key rate.","core_discovery":"The central claim is that the CMQC protocol distributes two-mode-squeezed (Gaussian) entanglement and classical information on the same optical mode. The decoupling trick is a continuous-variable teleportation performed by Bob: his homodyne outcomes are a noisy estimate of Alice's classical displacement, so he can recover the classical message while the entanglement is transferred to his retained mode. Classical bit errors make the final state non-Gaussian, but the contamination is exponentially small in the classical signal strength, and the ensemble state is captured by the covariance matrix V_out = [[a0 I, c0(1−δ)σZ], [c0(1−δ)σZ, (b0+Δ)I]], where Δ = 2α²τ e_C is the extra noise due to mis","pith_inferences":["One consequence left implicit is that a network of classical transceivers could maintain a background reservoir of entanglement with every other node, enabling on-demand QKD, teleportation, or distributed sensing without a dedicated quantum channel.","The use of reverse coherent information under a one-way protocol is the paper's most fragile step; replacing RCI with the forward-assisted capacity would either require two-way communication in the protocol or could substantially lower the predicted distillable-entanglement thresholds.","Gaussian extremality is invoked for a non-Gaussian mixture; a direct computation of the distillable entanglement of the exact non-Gaussian state (or a counterexample) would determine whether the lower bound is tight.","The sharp transition between distillable and non-distillable regimes as a function of e_C suggests a practical engineering rule: the classical signal-to-noise ratio at Bob's receiver must exceed a threshold set by the tolerable excess noise of the quantum layer."],"forward_implications":["Existing classical optical links could be upgraded to distribute CV entanglement while keeping the classical data stream, by adding an entanglement source and a teleporter at each node.","The protocol's classical bit-error rate can be tuned to a target (e.g., 10^-9) by increasing the modulation amplitude, at the cost of a large extra noise term 2d² e_C that kills entanglement beyond a loss threshold.","The point-to-point secret-key rate saturates the optimized CV-QKD bound only at very low error rates (e_C ≤ 10^-14), making the entanglement-based scheme more fragile to classical errors than the earlier SQCC-QKD approach.","The scheme naturally extends to repeater-like configurations by adding noiseless linear amplification and error-corrected re-displacement, allowing the hybrid signal to propagate over longer distances."],"fun_headline_variants":["Entanglement and classical bits co-travel on one channel","Single pulse carries classical data and Gaussian entanglement","Teleportation lets one channel send data and entanglement","Co-transmitting classical info and continuous-variable entanglement","Same fiber for classical messages and quantum entanglement"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The central bound on distillable entanglement is computed with the reverse coherent information, which assumes Bob may help via a backward classical channel, while the protocol is presented as one-way; the paper explicitly brackets this contradiction 'for practical reasons.'","fun_headline_variants_meta":{"raw":{"variants":["Entanglement and classical bits co-travel on one channel","Single pulse carries classical data and Gaussian entanglement","Teleportation lets one channel send data and entanglement","Co-transmitting classical info and continuous-variable entanglement","Same fiber for classical messages and quantum entanglement"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000193,"raw_usage":{"total_tokens":1169,"prompt_tokens":708,"completion_tokens":461,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":452,"completion_tokens_details":{"reasoning_tokens":388}},"tokens_in":452,"tokens_out":461,"duration_ms":4793,"temperature":1.0,"reasoning_tokens":388,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T03:11:14.300878+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute or measure the one-way distillable entanglement of the output state for parameters where the paper's RCI bound is positive (e.g., η=30 dB loss, ε=0.025 SNU, e_C=10^-6); if the forward-only distillable entanglement is zero while the RCI lower bound is positive, the claim that the protocol distributes distillable entanglement under one-way communication is falsified. Alternatively, an experimental attempt to distill EPR entanglement from the output state under one-way classical communication at 30 dB loss with e_C=10^-6 would settle it.","supporting_citations":[],"review_version":1}