{"id":"1d693123-2613-4f0f-9195-0e2c68cda3f6","arxiv_id":"2509.05727","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Classical and quantum optical skyrmions keep their skyrmion number through simulated atmospheric turbulence, while quantum entanglement drops.","lead":"This paper sends classical and quantum optical skyrmions through simulated atmospheric turbulence and finds their topological charge stays largely unchanged even as quantum entanglement degrades. The result could support turbulence-robust encoding of information in structured light.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Strict skyrmion-number conservation is not established: the coordinate-transformation proof in the supplement is asserted, not derived, and the paper's own far-field data show N decaying for the highest-order topology.","rationale":"The reader's verdict is already CONDITIONAL, and the identified weakest assumption—the existence of a smooth, invertible coordinate transformation in Supp. Eqs. S3–S5—is exactly the load-bearing gap I find. My stress test confirms and sharpens this concern: the transformation is asserted, not derived, and can fail at zeros of the denominator; the accompanying unitarity claim for one-sided channels is mathematically false; and the paper's own experimental data show N=5 decaying in the far-field and in propagation, undermining the 'strictly conserved' wording. These issues do not destroy the paper's contribution: the experiments demonstrate meaningful robustness for low and moderate turbulence and for most tested topologies, which is a valuable result. However, the central claim should be revised from strict conservation to approximate robustness within finite parameter ranges. Because the reader already recommends conditional acceptance with revision, my assessment does not change the verdict; hence UNCHANGED. I agree with the reader's weakest_assumption rather than disagreeing, and my concrete test would directly settle whether the coordinate-transformation mechanism is valid for the actual experimental realizations.","tokens_in":18111,"tokens_out":4517,"duration_ms":59397,"concrete_test":"Run a numerical survey using the same quantum state |Ψ⟩=(|0⟩|H⟩+|1⟩|V⟩)/√2 and the 200 turbulence realizations used for Fig. 2h. For each realization, compute the exact output conditional amplitude µ'(r,φ) from Eq. S2 using the spiral-imaging coefficients, locate all zeros of the denominator λ1|LG_0| + λ3|LG_1|e^{iφ}, and evaluate N directly by contour integration (Eq. S17). If any realization yields a denominator zero or a winding number different from 1 at Ω=1.2, the coordinate-transformation proof fails and 'strict conservation' is falsified for the tested channel.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim ('strictly conserved', Fig. 1) rests on the assertion that turbulence induces only a smooth, invertible coordinate transformation of the transverse plane, so that the output conditional amplitude µ'(r,φ) can be mapped to the input µ(r1,φ1) via Supp. Eqs. S3–S5. This is not proven. For the post-turbulence state, µ'(r,φ) = [λ2|LG_l1| + λ4|LG_l2|e^{i(l2−l1)φ}] / [λ1|LG_l1| + λ3|LG_l2|e^{i(l2−l1)φ}]. The denominator is a complex function of two real variables; it generically has isolated zeros where the Stokes texture is undefined and the map in Eq. S5 becomes singular or multi-valued. No argument is given that these zeros are absent for realistic turbulence-generated coefficients. Additionally, the main-text statement that 'any one-sided channel is unitary to any input pure state since it may be written as a positive trace-preserving map' is false: positive trace-preserving maps such as amplitude damping can send pure states to mixed states, and turbulence induces OAM crosstalk with an environment, so the reduced channel on photon A need not preserve purity. The paper's own experiments contradict strict conservation: in far-field turbulence (Fig. 3d), the mean measured N for the N=5 skyrmion visibly decays and error bars overlap at Ω=5, and in the propagation results (Fig. 3e) N=5 also decreases with increasing σ_R². The authors attribute this to difficulty in identifying singularities, but that concession means the measured invariant is not strictly conserved. What the data support is bounded, approximate robustness at low and moderate turbulence strength, not the strict topological protection claimed in the abstract and Fig. 1.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper reports classical and quantum optical skyrmion experiments in simulated atmospheric turbulence. The central claim is that the skyrmion number N, computed from the Stokes texture of a vectorially structured beam or from the conditional Stokes parameters of a hybrid-entangled two-photon state, remains 'strictly conserved' under turbulence, even as entanglement or classical correlations degrade. The authors present a theoretical argument based on coordinate-transformation invariance (Eq. 6 and Supplementary Eqs. S3–S5), supported by quantum state tomography of a BBO SPDC source and classical Stokes polarimetry with phase-screen turbulence, including near-field, far-field, and multi-phase-screen propagation channels.","tokens_in":18543,"tokens_out":7701,"duration_ms":82208,"significance":"The experimental scope is substantial: five topologies (N=1–5), several turbulence strengths, both single- and multi-phase-screen channels, and a direct classical–quantum comparison. If the robustness claim were established, the result would be valuable for turbulence-resilient structured-light communication and for the classical–quantum analogy of topological protection. The paper includes extensive experimental data and a reproducible-style methodology, and these are genuine strengths. However, the theoretical proof as written is incomplete, the false statement about trace-preserving maps is load-bearing, and the experimental data show deviations from strict conservation in the strongest tested cases. The headline claim therefore needs revision.","major_comments":[{"comment":"The statement 'Any one-sided channel is unitary to any input pure state since it may be written as a positive trace-preserving map, ensuring that the output must also be a pure state' is incorrect. Positive trace-preserving maps (CPTP maps) generally send pure states to mixed states (e.g., amplitude damping); unitarity is not implied by trace preservation. This claim underpins the purity-preservation argument for the output conditional state and the classical–quantum equivalence. The correct statement in this experiment is that a thin phase screen is a unitary transformation acting on the full spatial-mode Hilbert space of photon A, so the full two-photon state remains pure; the effective channel on the truncated OAM subspace is not unitary. Please correct the statement in the main text and the corresponding discussion.","section":"Main text, 'Classical-quantum equivalence of topologies'"},{"comment":"The proof of strict conservation rests on the existence of a global, smooth, invertible coordinate transformation χ(r,ϕ)=(r1,ϕ1) satisfying Eq. S3. Equation S5 provides local formulas, but no proof is given that χ is a bijection of R² with nonvanishing Jacobian and no zeros of the denominator λ1|LG_l1| + λ3|LG_l2|e^{i(l2−l1)ϕ}. At zeros the Stokes texture is undefined and the winding number is not protected; such zeros are generically expected for strong turbulence-generated coefficients. Because Eq. S5 is constructed so that µ'(r,ϕ)=µ(χ(r,ϕ)), and Eq. (6) makes N invariant under coordinate transformations by definition, the conclusion is built into the construction unless existence and regularity of χ are proven. This is the central load-bearing step and must be supplied, or the claim must be weakened.","section":"Supplementary Eqs. S3–S5"},{"comment":"The experimental data do not support strict conservation. In the far-field results (Fig. 3d), the mean measured N for the N=5 topology decays with Ω and the error bars overlap at Ω=5; in the single-phase-screen propagation results (Fig. 3e), N=5 also decreases with increasing σ_R². The text attributes this to difficulty in identifying singularities, but that concession means the measured invariant is not strictly conserved in the tested regime. The claim of strict conservation in Fig. 1 and the abstract should be replaced by a statement of approximate robustness over a specified parameter range, with an unbiased estimate of measurement uncertainty.","section":"Fig. 3d–e and Discussion"},{"comment":"The measured skyrmion number depends on the intensity threshold (3% of maximum) and the Gaussian filter kernel sizes (σ=1220 m⁻¹ far-field, σ=732 m⁻¹ propagation) introduced in post-processing. While these parameters are kept fixed across turbulence strengths, no sensitivity analysis is shown; different choices could remove real singularities or retain noise-induced singularities. Please provide a robustness check demonstrating that N is insensitive to these processing parameters, or quantify the bias they introduce in the strong-turbulence regime.","section":"Supplementary, Post-processing of classical experimental data"}],"minor_comments":[{"comment":"The transformation in Eq. S5 is described as conformal, but the radial and azimuthal transformations are generally coupled and depend on both r and ϕ; 'conformal' is inaccurate.","section":"Supplementary Eqs. S3–S5"},{"comment":"Typo: 'irregardless' should be 'regardless'.","section":"Supplementary, Post-processing of classical experimental data"},{"comment":"The Discussion repeats the statement that 'the unitary nature of any single-sided quantum channel' follows from trace preservation; this is the same error as in the main text and should be corrected.","section":"Discussion and Conclusion"},{"comment":"The blue shaded region representing the error range from 200 simulations is not defined in the caption; please specify whether it is a standard deviation, a confidence interval, or a full range.","section":"Fig. 2h"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper should be read for its experimental core, not its theoretical claims. The authors pass classical and quantum optical skyrmions (encoded N=1 to N=5) through simulated atmospheric turbulence in near-field, far-field, and 100 m propagation channels, extracting the skyrmion number via contour-integral Stokes polarimetry. The joint classical–quantum comparison under the same channel model is new, and the experiment is carefully done: 100 realizations per condition, error bars, and concurrence measured alongside N in the quantum case. That dataset is a useful benchmark for anyone working on structured light in turbulence.\n\nWhat the data actually show is bounded, approximate robustness. For weak to moderate turbulence, measured N stays close to the encoded value across all topologies. For the highest topology N=5 at the strongest far-field turbulence, the mean decays and error bars overlap. The authors acknowledge this but attribute it to difficulty in identifying singularities. That concession directly undermines the word 'strictly conserved' used in the abstract and Figure 1.\n\nThe theory has deeper problems. The statement that any one-sided positive trace-preserving channel is unitary on pure inputs and preserves purity is false; amplitude damping is a counterexample, and the paper's own concurrence measurements show the state becoming mixed. The coordinate-transformation proof in the supplement is asserted, not derived. Equations S3–S5 construct a map from output to input coordinates, and since the skyrmion number is coordinate-invariant by definition, the conclusion is built in. No argument establishes that this map is smooth, single-valued, and free of singularities once turbulence introduces cross-talk. The denominator in Eq. S2 can generically vanish, leaving the Stokes texture undefined.\n\nThese are load-bearing flaws in the theoretical framing, not cosmetic issues. The qualitative insight — that topological charge survives turbulence better than entanglement or spatial correlations — is probably right in the tested regime, and the experiments support it. But the strong claim needs either a real proof of the coordinate transformation or a significant softening to 'approximate robustness under weak-to-moderate turbulence.'\n\nThe paper deserves a serious referee. The editor should not desk-reject it; the experimental work is substantial and the physics is interesting. But the referee should push hard on the theory and on the strict-conservation wording. I would bring it to a reading group as a case study in how experimental cleverness can outrun theoretical justification, and I would cite the experimental results with a caveat.","headline":"Solid experimental demonstration of skyrmion robustness under turbulence, but the 'strict conservation' claim overreaches; the data support bounded, approximate robustness.","tokens_in":19024,"tokens_out":2984,"would_cite":true,"duration_ms":35185,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that the skyrmion number of optical skyrmions, whether built from classical vector beams or from entangled photon pairs, stays fixed when the light passes through simulated atmospheric turbulence, even though the turbulenc","keywords":["optical skyrmions","atmospheric turbulence","topological protection","Stokes parameters","orbital angular momentum","quantum entanglement","structured light","skyrmion number"],"falsifier":"Propagate a skyrmion with |ℓ1| ≠ |ℓ2| through a turbulent channel strong enough that the denominator λ1|LG_ℓ1| + λ3|LG_ℓ2| e^{i(ℓ2−ℓ1)φ} vanishes at some point in the transverse plane; then measure whether the contour-integral value of the skyrmion number N deviates from the encoded value or becomes undefined.","tokens_in":17996,"feed_emoji":"🌀","tokens_out":4189,"duration_ms":41373,"temperature":0.7,"pith_summary":"This paper asks whether the skyrmion number—a topological charge computed from the Stokes texture of a structured light field—survives propagation through atmospheric turbulence. The authors build quantum optical skyrmions from hybrid-entangled OAM-polarization photon pairs and classical vector beams, send them through experimentally simulated turbulent channels, and measure the skyrmion number before and after. They find that although turbulence scrambles the spatial structure and degrades entanglement or classical correlations, the skyrmion number remains unchanged. The result matters because it offers a topological degree of freedom that could carry information robustly through noisy free-space channels. The paper also gives a theoretical explanation: turbulence is a one-sided channel acting only on the spatial mode, and its effect can be represented as a smooth coordinate transformation under which the skyrmion number is invariant.","feed_headline":"Skyrmion number survives atmospheric turbulence","feed_subtitle":"Topological charge holds for classical beams and entangled photons even as entanglement degrades.","key_machinery":"The skyrmion number, N = (1/4π)∫ ε_ijk S_i (∂S_j/∂x)(∂S_k/∂y) dxdy, computed from locally normalized Stokes parameters S_i, is a winding number counting how many times the spin texture wraps the Poincaré sphere. For the state family |Ψ⟩ = λ_1|ℓ1⟩_A|H⟩_B + λ_2|ℓ2⟩_A|V⟩_B, the formula simplifies to N = n|ℓ1 − ℓ2|, so the charge is set by the OAM difference. The turbulence channel is one-sided: it acts on the spatial mode (photon A) but not on polarization (photon B), and is represented by a positive trace-preserving map that leaves the output pure. The quantum proof then absorbs the turbulence-induced mode mixing into a coordinate transformation (r, φ) → (r₁, φ₁) satisfying a conformal conditi","core_discovery":"The central claim is that the skyrmion number N, computed from the conditional Stokes parameters of a hybrid-entangled two-photon state or from the Stokes texture of a classical vector beam, is conserved under atmospheric turbulence. Turbulence-induced OAM scattering changes the spatial modes, yet the output spin texture still wraps the same number of times around the Poincaré sphere. The authors argue this in the quantum setting by invoking the invariance of the skyrmion number under coordinate transformations: turbulence is modeled as a one-sided channel that distorts only the spatial degree of freedom, and the disturbance can be absorbed into a smooth reparametrization of the transverse p","pith_inferences":["If the invariance holds beyond the tested parameter range, the skyrmion number could serve as a noise-resilient encoding basis for quantum key distribution, where a bit value is assigned to N rather than to a specific OAM value.","The one-sided channel argument suggests the result should generalize to other disturbances acting on only one degree of freedom, such as some scattering or defocusing; however, the existence of the coordinate transformation has not been proven for all turbulence strengths, so testing under extreme scintillation would probe the limit.","An untested practical limit is whether protection persists when both photons pass through separate turbulent channels (a two-sided channel), where the one-sided purity argument no longer applies."],"forward_implications":["Turbulence can be treated as a one-sided channel, so any hybrid entangled state with spatial and polarization degrees of freedom is expected to keep its topological charge even when entanglement degrades.","The skyrmion number N is a basis-independent observable derived from four Stokes intensity measurements, and the measured value distinguishes topologies N=1 through N=5 across a simulated 100 m turbulent channel.","Since N survives both near-field phase distortions and far-field scintillation at moderate strengths, it is a candidate degree of freedom for encoding information in free-space optical links.","Higher-order topologies (e.g., N=5) show measurable decay in strong far-field turbulence, so topology-based encoding has a practical strength ceiling.","The non-separability framework connects classical vector beams and quantum entangled biphoton states, allowing robustness results to transfer between the two regimes."],"supporting_citations":[{"why":"Supplies the quantum skyrmion state and its Stokes parameter formulation for hybrid-entangled biphoton systems.","marker":"[33]"},{"why":"Provides the general quantum-channel treatment of quantum skyrmions that the robustness claim extends.","marker":"[41]"},{"why":"Gives the spiral imaging / OAM scattering model used to describe turbulence effects on spatial modes.","marker":"[44]"},{"why":"Derives the paraxial skyrmionic beam formalism and the skyrmion number integral used throughout.","marker":"[19]"},{"why":"The contour-integral method used to compute the skyrmion number from experimental Stokes data.","marker":"[57]"},{"why":"Supplies the phase-screen simulation approach, Rytov variance scaling, and digital implementation used in the classical experiments.","marker":"[48]"},{"why":"Establishes the classical-quantum equivalence of non-separable states, grounding the one-sided channel analogy.","marker":"[38]"},{"why":"Channel-state duality used to justify treating any one-sided channel as a unitary transformation on the input pure state.","marker":"[39]"},{"why":"Provides the post-processing calibration routine for classical skyrmion-number extraction from noisy camera data.","marker":"[68]"}],"fun_headline_variants":["Skyrmion number immune to atmospheric turbulence","Optical skyrmions keep their topological charge in turbulence","Turbulence scrambles light but not skyrmion topology","Classical and quantum skyrmions shake off turbulence","Structured light's skyrmion count survives atmospheric chaos"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The protection proof assumes every turbulence-induced spatial distortion can be undone by a single smooth, invertible coordinate change of the transverse plane, a transformation that is not proven to exist when the texture's amplitude denominator vanishes.","fun_headline_variants_meta":{"raw":{"variants":["Skyrmion number immune to atmospheric turbulence","Optical skyrmions keep their topological charge in turbulence","Turbulence scrambles light but not skyrmion topology","Classical and quantum skyrmions shake off turbulence","Structured light's skyrmion count survives atmospheric chaos"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000232,"raw_usage":{"total_tokens":1306,"prompt_tokens":705,"completion_tokens":601,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":449,"completion_tokens_details":{"reasoning_tokens":537}},"tokens_in":449,"tokens_out":601,"duration_ms":6470,"temperature":1.0,"reasoning_tokens":537,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T05:07:07.489985+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Propagate a skyrmion with |ℓ1| ≠ |ℓ2| through a turbulent channel strong enough that the denominator λ1|LG_ℓ1| + λ3|LG_ℓ2| e^{i(ℓ2−ℓ1)φ} vanishes at some point in the transverse plane; then measure whether the contour-integral value of the skyrmion number N deviates from the encoded value or becomes undefined.","supporting_citations":[{"cited_title":"Non-local skyrmions as topologically resilient quantum entangled states of light,","cited_arxiv_id":null,"evidence_quote":"Supplies the quantum skyrmion state and its Stokes parameter formulation for hybrid-entangled biphoton systems."},{"cited_title":"Quantum skyrmions in general quantum channels,","cited_arxiv_id":null,"evidence_quote":"Provides the general quantum-channel treatment of quantum skyrmions that the robustness claim extends."},{"cited_title":"Robust struc- tured light in atmospheric turbulence,","cited_arxiv_id":null,"evidence_quote":"Gives the spiral imaging / OAM scattering model used to describe turbulence effects on spatial modes."},{"cited_title":"Paraxial skyrmionic beams,","cited_arxiv_id":null,"evidence_quote":"Derives the paraxial skyrmionic beam formalism and the skyrmion number integral used throughout."},{"cited_title":"Analysis codes for vector mode in unitarity channel,","cited_arxiv_id":null,"evidence_quote":"The contour-integral method used to compute the skyrmion number from experimental Stokes data."},{"cited_title":"Spa- tially resolving classical and quantum entanglement with structured photons,","cited_arxiv_id":null,"evidence_quote":"Supplies the phase-screen simulation approach, Rytov variance scaling, and digital implementation used in the classical experiments."},{"cited_title":"Classically en- tangled light,","cited_arxiv_id":null,"evidence_quote":"Establishes the classical-quantum equivalence of non-separable states, grounding the one-sided channel analogy."},{"cited_title":"Channel-state duality,","cited_arxiv_id":null,"evidence_quote":"Channel-state duality used to justify treating any one-sided channel as a unitary transformation on the input pure state."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the post-processing calibration routine for classical skyrmion-number extraction from noisy camera data."}],"review_version":1}