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REVIEW 4 major objections 4 minor 70 references

Topological robustness of classical and quantum optical skyrmions in atmospheric turbulence

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read 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

desk verdict Solid experimental demonstration of skyrmion robustness under turbulence, but the 'strict conservation' claim overreaches; the data support bounded, approximate robustness. read the letter →

arxiv 2509.05727 v1 pith:LLHEPSR5 submitted 2025-09-06 physics.optics physics.app-phquant-ph

Zhenyu Guo , Cade Peters , Nilo Mata-Cervera , Anton Vetlugin , Ruixiang Guo , Pei Zhang , Andrew Forbes , Yijie Shen This is my paper
classification physics.opticsphysics.app-phquant-ph
keywords opticalskyrmionsatmosphericturbulencetopologicalprotectionStokesparametersorbitalangularmomentumquantumentanglementstructuredlightskyrmionnumber
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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

What would settle it

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.

Watch

Extended reading notes

Core claim

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

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

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.

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 (4)
  1. [Main text, 'Classical-quantum equivalence of topologies'] 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.
  2. [Supplementary Eqs. S3–S5] 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.
  3. [Fig. 3d–e and Discussion] 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.
  4. [Supplementary, Post-processing of classical experimental data] 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.
minor comments (4)
  1. [Supplementary Eqs. S3–S5] 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.
  2. [Supplementary, Post-processing of classical experimental data] Typo: 'irregardless' should be 'regardless'.
  3. [Discussion and Conclusion] 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.
  4. [Fig. 2h] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the skyrmion-number conservation argument is a conditional constructive proof, not a fit or self-citation chain; the paper's own experiments independently support the measured robustness.

full rationale

I walked the paper's derivation chain. The central claim is that the skyrmion number N is conserved under simulated atmospheric turbulence, for both quantum and classical states. The theoretical support is Eq. (6), the invariance of N under coordinate transformations, combined with the supplementary construction (Eqs. S3–S5) of a coordinate map r1(r,ϕ), ϕ1(r,ϕ) such that the output conditional amplitude µ′(r,ϕ) equals the input amplitude µ(r1,ϕ1). This is a constructive equivalence proof: if such a map exists and is a smooth, invertible, orientation-preserving transformation, then N is indeed conserved by the standard topological-degree argument. The map is not fitted to data; it is an explicit algebraic solution. Therefore the conclusion is not equivalent to the inputs by construction, in contrast to a fitted parameter renamed as a prediction. The experimental and numerical results are independent of that proof: the quantum N values are computed from tomographically reconstructed density matrices, the classical N values from full Stokes polarimetry, and the theoretical curves in Fig. 2h come from 200 independent turbulent-screen simulations. No fitted parameter is renamed as a prediction. The paper contains several self-citations (Refs. 33, 40, 41, 68) with overlapping authorship, but none of them is load-bearing in the circularity sense. The core derivation is presented in the supplement rather than merely imported from prior work, and the cited prior experimental results (e.g., quantum skyrmion states, invariance of vectorial structured light) are externally falsifiable and not the sole support for the present claim. There are legitimate correctness concerns that are not circularity. The supplement asserts the existence of the coordinate transformation without proving that it is globally single-valued and nonsingular; the denominator λ1|LG_l1|+λ3|LG_l2|e^{i(l2−l1)ϕ} can vanish, leaving the Stokes texture undefined. The main-text statement that a positive trace-preserving map must be unitary and preserve purity is mathematically false. The paper itself concedes measured deviations for the highest-order topology N=5 in far-field turbulence, attributing them to difficulty in identifying singularities. These are rigor and evidentiary limitations, not instances of the derivation reducing to its own inputs. Hence the circularity score is 0.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central theoretical claim draws on standard homotopy invariance but also on several assumptions specific to this paper. The most important is that turbulence on the OAM degree of freedom can be represented as a coordinate transformation of the transverse plane; this assumption is introduced to prove the quantum result and is not independently validated. The two-mode truncation and the radial profile simplification are additional unstated choices. The data-processing thresholds and the choice of polarization field P2/P3 are free parameters that affect N.

free parameters (3)
  • Intensity noise threshold (3% of max) = 0.03 x I_max
    Used in all classical N calculations to discard singularities in low-intensity regions; calibrated on noise floor of unaberrated beams (Supplementary 'Post-processing').
  • Gaussian filter kernel sigma = 1220 m^-1 (far-field), 732 m^-1 (propagation)
    Low-pass filter applied before singularity search; kernel chosen to suppress high-frequency intensity features and kept constant per configuration.
  • Polarization field choice (P2/P3 vs P1) = P2=S3+iS1, P3=S1+iS2
    P1 exhibited erratic behaviour over realizations and was excluded; this selection affects which singularities are counted (Supplementary 'Polarization singularities').
assumptions (6)
  • standard math Skyrmion number is invariant under smooth coordinate transformations of the transverse plane
    Used in Eq. (6) to argue topological robustness; standard homotopy invariance of mapping degree.
  • domain assumption Atmospheric turbulence affects only the spatial (OAM) degree of freedom, not polarization
    One-sided channel assumption at start of Results; reasonable for propagation in air.
  • ad hoc to paper Turbulence-induced scattering can be represented by a global conformal coordinate transformation satisfying µ(r1,φ1)=µ'(r,φ)
    Supplementary Eqs. S3-S5; existence, invertibility and non-singularity are not proven, and this assumption carries the whole quantum robustness argument.
  • ad hoc to paper The two-mode OAM subspace {l1,l2} is sufficient to determine the topological response under turbulence
    Eq. (5) truncates the scattered state to qubit space; higher OAM modes are dropped before computing Stokes texture and N.
  • domain assumption LG radial profile for epsilon(r) is r^{|l2|-|l1|} with no Laguerre polynomial dependence
    Supplementary Eq. S4 simplification; only valid for radial index p=0, not stated.
  • ad hoc to paper A one-sided positive trace-preserving map acts unitarily on pure input states and preserves purity
    This false premise is used to write the output as a ket and to argue quantum-classical equivalence; contradicted by the paper's own concurrence data (Fig. 2h).

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Pith. "Pith review of Topological robustness of classical and quantum optical skyrmions in atmospheric turbulence." pith.science (2026). https://pith.science/paper/LLHEPSR5

@misc{pith2026250905727,
  author       = {Pith},
  title        = {Pith review of: Topological robustness of classical and quantum optical skyrmions in atmospheric turbulence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LLHEPSR5}},
  note         = {Machine review of arXiv:2509.05727}
}
read the original abstract

The degradation of classical and quantum structured light induced by complex media constitutes a critical barrier to its practical implementation in a range of applications, from communication and energy transport to imaging and sensing. Atmospheric turbulence is an exemplary case due to its complex phase structure and dynamic variations, driving the need to find invariances in light. Here we construct classical and quantum optical skyrmions and pass them through experimentally simulated atmospheric turbulence, revealing the embedded topological resilience of their structure. In the quantum realm, we show that while skyrmions undergo diminished entanglement, their topological characteristics maintain stable. This is paralleled classically, where the vectorial structure is scrambled by the medium yet the skyrmion remains stable by virtue of its intrinsic topological protection mechanism. Our experimental results are supported by rigorous analytical and numerical modelling, validating that the quantum-classical equivalence of the topological behaviour is due to the non-separability of the states and one-sided nature of the channel. Our work blurs the classical-quantum divide in the context of topology and opens a new path to information resilience in noisy channels, such as terrestrial and satellite-to-ground communication networks.

Figures

Figures reproduced from arXiv: 2509.05727 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. d and e, N = 5 demonstrates a small but no￾ticeable decay as the aberration strength increases. This can be attributed to the fact that higher order topolo￾gies exhibit polarisation structures that change rapidly across the transverse plane. When these structures are distorted and no longer symmetrical, it can be challeng￾ing to reliably identify all of the polarisation singulari￾ties needed to accurately determine … view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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