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Cited by 52Quantum Information and CryptographyQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications

The DOI matches its Crossref record; 50 of the 50 references it cites were found in a registry or an index; 1 of the 6 sources its claims cite were checked for support.

Topological rejection of noise by quantum skyrmions

Open access
Ornelas, Pedro, Nape, Isaac, de Mello Koch, Robert, Forbes, Andrew·2025·Nature Communications
DOI 10.1038/s41467-025-58232-4PMC PMC11937260
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Abstract

An open challenge in the context of quantum information processing and communication is improving the robustness of quantum information to environmental contributions of noise, a severe hindrance in real-world scenarios. Here, we show that quantum skyrmions and their nonlocal topological observables remain resilient to noise even as typical entanglement witnesses and measures of the state decay. This allows us to introduce the notion of digitization of quantum information based on our discrete topological quantum observables, foregoing the need for robustness of entanglement. We compliment our experiments with a full theoretical treatment that unlocks the quantum mechanisms behind the topological behavior, explaining why the topology leads to robustness. Our approach holds exciting promise for intrinsic quantum information resilience through topology, highly applicable to real-world systems such as global quantum networks and noisy quantum computers. Recent work reported a non-local quantum entangled state of photons with skyrmionic topology. Here the authors demonstrate theoretically and experimentally that topological properties of this system are resilient to noise, even as entanglement measures decay, and elucidate the mechanisms behind this robustness.

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

The paper shows theoretically and experimentally that quantum skyrmions and their nonlocal topological observables remain invariant under isotropic noise even as entanglement witnesses decay, collapsing only when entanglement vanishes. This suggests digitized topological quantum information can be robust without error mitigation.

Key findings

  • The Skyrmion number remained stable under isotropic noise for six initial topologies \(N \in \{-3,-2,-1,1,2,3\}\); for an example state, \(N = 2.99 \pm 0.01\) at purity \(\gamma = 0.80\) and \(\gamma = 0.45\), then collapsed to \(N = 0.01 \pm 0.01\) at the maximally mixed limit \(\gamma = 0.25\).
  • Typical entanglement witnesses decayed continuously: concurrence reached \(C = 0\), fidelity \(F = 0.25\), and purity \(\gamma = 0.25\) for a 2D maximally mixed state, while the Skyrmion number stayed intact until entanglement vanished.
  • The no-noise example state had purity \(\gamma = 0.80\) and Skyrmion number \(N = 0.96 \pm 0.01\) (theory \(N = 1\)); quantum contrast \(Q_c\) ranged from 32.3 to 2.24, and purity versus \(Q_c\) agreed with theory with mean-squared error 0.02.
  • Topological robustness held across Neél-type, anti-skyrmion, and higher-order skyrmion/anti-skyrmion textures; noise acted as a smooth deformation that scaled the quantum Stokes vectors without changing their orientation.

Methods

  • Theory: a bi-photon entangled state \(\lvert\Psi\rangle = 1/\sqrt{2}(\lvert\ell_1\rangle_A\lvert P_1\rangle_B + e^{i\delta}\lvert\ell_2\rangle_A\lvert P_2\rangle_B)\) with \(\lvert\ell_1\rvert \neq \lvert\ell_2\rvert\); isotropic noise modeled as \(\rho = p\lvert\Psi\rangle\langle\Psi\rvert + (1-p)/4\,\mathbb{1}_4\), with purity \(\gamma = p^2 + (1-p^2)/4\), and Skyrmion number computed from quantum Stokes parameters.
  • Experiment: entangled OAM biphotons at 710 nm generated by SPDC in a 3 mm Type-I BBO crystal pumped at 355 nm, with Schmidt number \(K = 11\); spatial-to-polarization coupling prepared hybrid states, and six projective measurements per photon gave a 36-entry quantum state tomography.
  • Analysis: reconstructed density matrices were used to compute quantum Stokes vectors and Skyrmion numbers, compared against concurrence, fidelity, and purity across noise levels set by an incoherent light source and quantified by quantum contrast \(Q_c\).

Limitations

  • Stated: the spatial-to-polarization coupling efficiency limited hybrid state creation to OAM values \(\lvert\ell\rvert \leq 3\), though the authors note losses may be mitigated by more compact and efficient dynamic spin-orbit coupling techniques.
  • Stated: minor deviations at higher noise levels likely arose from random noisy detector contributions and small fluctuations between projective measurements averaged to determine quantum contrast.
  • Evident: the density-matrix treatment restricts to the original two-dimensional OAM subspace and uses an isotropic noise model; no test of non-isotropic or structured noise is reported.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/s41467-025-58232-4

Cites

50 of 50 references verified0 citation errors · 0 not checkable

Statistics

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Verification

Claims the paper makes

1 of 6 cited sources checked · 1 supported · 0 flagged

  • Findingnone given

    The magnitude of the quantum Stokes vector diminishes with decreasing purity (increasing noise), until it collapses to a point with zero magnitude.

    “As expected, the magnitude of the quantum Stokes vector diminishes with decreasing purity (increasing noise), until it collapses to a point with zero magnitude.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    The Skyrmion number remains constant in the presence of isotropic noise despite the decay of the initial state and typical entanglement witnesses, until the state becomes maximally mixed.

    “This invariance is depicted in Fig. 2b where the Skyrmion number remains constant in the presence of noise despite the decay of the initial state, quantified by a decrease in typical entanglement witnesses.”
    • Also stated in: § Experiment · plain
      “The Skyrmion number for these three states (1–3) was calculated to be N = 2.99 ± 0.01, N = 2.99 ± 0.01 and N = 0.01 ± 0.01, respectively, revealing that the skyrmion number remains intact until the entanglement vanishes altogether.”
    • Also stated in: § Quantum skyrmions · plain
      “The Skyrmion number is a digitized observable, shown here for integer values from N = −2 to N = 2, remaining intact along with the topology after the isotropic noise even while the entanglement decreases, except in the case when the entanglement reaches its minimum, indicating a non-entangled state.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).
  • Findingown data

    The experimentally obtained purity plotted against average quantum contrast is in excellent agreement with theory, with a calculated mean-squared error of 0.02.

    “In Fig. 4 the experimentally obtained purity is plotted against average quantum contrast and is in excellent agreement with theory with a calculated mean-squared error of 0.02, with minor deviations occurring at higher noise levels likely occurring from random noisy detector contributions and small fluctuations between projective measurements which are averaged over to determine the quantum contra”
    Quote in the paperSubstantial claim
  • Findingnone given

    The demonstrated resilience comes without the need for error mitigation or state purification techniques.

    “The demonstrated resilience comes without the need for error mitigation or state purification techniques, thus offering an approach to quantum information resilience in realistic and non-ideal conditions.”
    Quote in the paperSubstantial claim
  • Findingcitation

    When the state is maximally mixed (γ=1/4), the Skyrmion number vanishes (N=0) because there is no entanglement and thus no non-trivial topology.

    “When the state is maximally mixed, γ=1/4, the calculated Skyrmion number vanishes as the radius of the shell has reduced to zero.”
    • Also stated in: § Experiment · boosted
      “The zoomed inset shows experimental data near the classical limit where it is clear that a topological transition from N ≠ 0 to N = 0 occurs because without entanglement there can be no topology.”
    • Also stated in: § Quantum skyrmions · plain
      “Once the state is maximally-mixed, the Hilbert space of photon B has zero radius, no entanglement, and thus only a trivial topology (N = 0).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [43] Ornelas, P., Nape, I., de Mello Koch, R. & Forbes, A. Non-local skyrmions as topologically resilient quantum entangled states of light. Nat. Photon. 18, 258–266 (2024). source

      A check is scheduled.

    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).
  • It may state two separate claims as one. 12
  • The quote only partly states this claim. 3
  • Probably not a substantial claim. 5

  • It may state two separate claims as one.

    Premisecitation

    When |l1| ≠ |l2| the bi-photon correlations form the desired skyrmionic mapping from R2 to S2, so that the entanglement defines a topology.

    “When ∣ℓ1∣ ≠ ∣ℓ2∣ the bi-photon correlations form the desired skyrmionic mapping from R²→S², so that the entanglement defines a topology43.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [43] Ornelas, P., Nape, I., de Mello Koch, R. & Forbes, A. Non-local skyrmions as topologically resilient quantum entangled states of light. Nat. Photon. 18, 258–266 (2024). source

  • It may state two separate claims as one.

    Findingown data

    Typical entanglement witnesses such as concurrence, fidelity, and state purity decay continuously under noise until they reach their expected minima for a 2D maximally mixed state (C=0, F=0.25, γ=0.25), while the Skyrmion number remains intact regardless of the degree of noise present, only decaying once the state is maximally mixed.

    “While each of the entanglement witnesses decay continuously until they each reach their expected minima for a 2D maximally mixed state (C = 0, F = 0.25, γ = 0.25), the Skyrmion number remains intact regardless of the degree of noise present, only decaying once the state is maximally mixed.”
    • Also stated in: § Experiment · plain
      “While the Skyrmion number is stable to noise, typical entanglement witnesses such as concurrence, fidelity and purity are not, as shown experimentally (points) and theoretically (lines).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).

  • It may state two separate claims as one.

    Findingown data

    The topology remains unchanged as noted by the position, length and orientation of the vectors, resulting in an almost unchanged Skyrmion number in excellent agreement with the ideal case.

    “We see that the topology remains unchanged as noted by the position, length and orientation of the vectors, resulting in an almost unchanged Skyrmion number that is in excellent agreement with the ideal case (within experimental uncertainty).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).

  • It may state two separate claims as one.

    Findingown data

    The QST reveals a characteristic saturation of each projection measurement with an increase in isotropic noise, accompanied by a transition of the density matrix from pure (entangled) to maximally mixed (no entanglement).

    “Furthermore, the QST reveals a characteristic saturation of each projection measurement with an increase in isotropic noise. This is accompanied by a clear transition of the density matrix describing a pure state (entangled) to that describing a maximally-mixed state (no entanglement) as shown in Fig. 5b.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    The theoretical and experimental results for the Skyrmion number as a function of quantum contrast are in excellent agreement across all topologies, providing evidence for topological robustness across all topological classes.

    “The theoretical (dashed lines) and experimental (points) results for the Skyrmion number as a function of quantum contrast are in excellent agreement across all topologies, providing further evidence for topological robustness across all topological classes.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).

  • It may state two separate claims as one.

    Findingown data

    The experimentally reconstructed state for |Ψ⟩=1/√2(|1⟩A|H⟩B+|0⟩A|V⟩B) has purity γ=0.80 and Skyrmion number N=0.96±0.01, in agreement with theory N=1.

    “The data is in agreement with the results expected from the desired pure state, with a purity of γ = 0.80 and Skyrmion number N = 0.96 ± 0.01 (theory: N = 1).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).

  • The quote only partly states this claim.

    Findingown data

    Quantum skyrmions and their nonlocal topological observables remain resilient to isotropic noise even as typical entanglement witnesses and measures of the state decay.

    “Here, we show that quantum skyrmions and their nonlocal topological observables remain resilient to noise even as typical entanglement witnesses and measures of the state decay.”
    • Also stated in: § Introduction · plain
      “Here we show both theoretically and experimentally that quantum skyrmions and their topological quantum observables remain resilient to noise even as typical entanglement witnesses and quantum observables of the state decay.”
    • Also stated in: § Discussion · boosted
      “In conclusion, we have shown both theoretically and experimentally that quantum skyrmions and their topological quantum observables remain resilient to isotropic noise, a generic form of quantum noise that captures realistic effects from the source, channel, and detector, e.g., multi-photon events, dark counts, shot and thermal noise, background light (e.g., daylight) and lost photons.”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Findingown data

    The importance of our work is that, for a physical and realistic source of noise, we have been able to demonstrate that noise is not able to drive the jumps between discrete states that would corrupt the discrete signal.

    “The importance of our work is that, for a physical and realistic source of noise, we have been able to demonstrate this.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    The experimental state vectors exhibit minimal deviation from the ideal case; the noise acts only to scale the vectors, not to change their orientation.

    “The experimental state vectors exhibit minimal deviation from the ideal case as the noise acts only to scale the vectors, not to change their orientation.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).

  • It may state two separate claims as one. The quote only partly states this claim.

    Findingown data

    For the example state |Ψ⟩=1/√2(|3⟩A|H⟩B+|0⟩A|V⟩B), the Skyrmion numbers for pure (γ=0.80), partially mixed (γ=0.45), and maximally mixed (γ=0.25) states are N=2.99±0.01, N=2.99±0.01, and N=0.01±0.01, respectively.

    “The Skyrmion number for these three states (1–3) was calculated to be N = 2.99 ± 0.01, N = 2.99 ± 0.01 and N = 0.01 ± 0.01, respectively, revealing that the skyrmion number remains intact until the entanglement vanishes altogether.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).

  • Probably not a substantial claim.

    Interpretationnone given

    The analysis does not assume anything about the initial pure state under investigation.

    “Importantly, this analysis does not assume anything about the initial pure state under investigation.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisereasoning

    Discrete signals are always more robust against the effects of noise because noise must flip the signal between two discrete states before any effect is registered.

    “Discrete signals are always more robust against the effects of noise. This follows because for discrete signals the noise can’t produce an arbitrarily small perturbation of the signal: the noise must be able to flip the signal between two discrete states before any effect is registered.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    This does not change the topology: R2 still maps to a sphere S2, albeit one of a smaller radius, with the same Skyrmion number.

    “This does not change the topology: R² still maps to a sphere S², albeit one of a smaller radius, with the same Skyrmion number.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).

  • Probably not a substantial claim.

    Premisecitation

    A generic (isotropic) noise model, by mixing the initially pure state with a maximally mixed state, is a common way to simulate real-world noisy conditions and covers a wide range of random noise sources.

    “A common way to simulate real-world noisy conditions is to use a generic (isotropic) noise model, by mixing the initially pure state with a maximally mixed state49, covering a wide range of random noise sources e.g., from the source (multi-photon events), the channel (background and lost photons), and the detector (dark counts).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [49] Dür, W., Briegel, H.-J., Cirac, J. I. & Zoller, P. Quantum repeaters based on entanglement purification. Phys. Rev. A 59, 169 (1999). source

  • Probably not a substantial claim.

    Interpretationreasoning

    Our approach to noise rejection can be understood in the context of information digitization, where continuous analogue signals are replaced by a discrete signal of bits through binning.

    “Our approach to noise rejection can be understood in the context of information digitization, where continuous analogue signals are replaced by a discrete signal of bits through binning, e.g., by declaring signals below some threshold as 0 and those above it as 1.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Interpretationnone given

    The topology of the wavefunction with its associated discrete observable naturally achieves discretization of entanglement.

    “We moot that the topology of the wavefunction with its associated discrete observable naturally achieves this.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Interpretationnone given

    The isotropic noise model makes no assumptions about the photons' degrees of freedom and can be extended to investigate its impact on higher-dimensional states.

    “Moreover, the isotropic model employed in this work makes no assumptions about the photons’ degrees of freedom and can be extended to investigate its impact on higher-dimensional states.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    Quantum channels are map preserving: they can be viewed as a smooth deformation of the state and thus preserve topology even when the entanglement itself is decaying.

    “confirming that such quantum channels are map preserving: they can be viewed as a smooth deformation of the state (map) and thus preserves topology even when the entanglement itself is decaying.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).
18 of 18

  • The authors state this as an assumption.

    The sphere of quantum Stokes parameters is normalized to the unit sphere (Σ Si²=1).

    “it is assumed that the sphere has been normalized such that Σi=1³Si²=1, i.e., a mapping to the unit sphere.”

  • The authors state this as an assumption.

    The restriction to the original two-dimensional OAM subspace of photon A is without loss of generality.

    “Without loss of generality we restrict ourselves to the original two dimensional OAM subspace of the Hilbert space of photon A so that the density matrix can be written as3 ρ=p∣Ψ⟩⟨Ψ∣+(1−p)/414”

  • The paper relies on this without support.

    All topological states are entangled, but not all entangled states are topological.

    “The motivation is that all topological states are entangled, but not all entangled states are topological.”
3 of 3

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Nonlocal quantum skyrmions are immune to the effects of entanglement decay and isotropic noise.

    “Likewise, it has also been demonstrated that nonlocal quantum skyrmions are immune to the effects of entanglement decay (57) and isotropic noise (58).”

    From Topological robustness of optical skyrmions through a real-world free-space link (2026) · cites this paper as [58]

    The Introduction and Discussion report that nonlocal quantum-skyrmion topology remains resilient to isotropic noise while entanglement measures decay. But the Discussion says the topology collapses once no entanglement remains, so the unqualified claim of immunity overstates the result. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • A state with purity 0.80 is called pure

    Minor

    The paper's purity formula gives γ=1 for a pure state (p=1). Point 1, reported as γ=0.80, is therefore not pure under the paper's own definition.

1 of 1

Citations

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. Nielsen, M. A. & Chuang, I. L. Quantum computation and quantum information (Cambridge university press, 2001).

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Related

Metadata

Authors
Ornelas, P., Nape, I., de Mello Koch, R., & Forbes, A.
Affiliations
University of the Witwatersrand (ZA)
Corresponding author
Forbes, Andrew
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2025-03-26
Volume
16
Issue
1
Pages
2934-2934
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-025-58232-4
PMC
PMC11937260
OpenAlex
W4408877573
Semantic Scholar
9afdc82862344a44b521438d1face34d214485c8
Cited by
52
References
50
Citations by year
2026: 30 · 2025: 21
FWCI
14.91
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by-nc-nd)
  • PubMed Central (publishedVersion, cc-by-nc-nd)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University) (cc-by)
Funders
National Research Foundation
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
quantum skyrmions, noise robustness, entanglement decay, entanglement witnesses, topological protection, noisy quantum computers

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