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Quantum skyrmions in general quantum channels

de Mello Koch, Robert, Lu, Bo-Qiang, Ornelas, Pedro, Nape, Isaac, Forbes, Andrew·2025·APL Quantum
DOI 10.1063/5.0271868
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Abstract

Quantum skyrmions as topologically structured entangled states have the potential to be a pathway toward robustness against external perturbations, but so far no theoretical framework exists to validate this. Here, we introduce the notion of a new entanglement observable based on such topologies and develop a theoretical framework for studying its evolution in general quantum channels. Using photons entangled in orbital angular momentum and polarization as an example, we show that the noise affecting both photons can be recast as a position-dependent perturbation affecting only the photon in the polarization state, restricting the noise to a finite-dimensional Hilbert space. From this we predict complete resilience for both non-depolarizing and depolarizing noise, the former by rigorous arguments based on homotopic maps and the latter by numerical simulation. Finally, we identify sources of local noise that can destabilize the topology and suggest why this may be ignored in practical situations. Our work sets a solid foundational framework for understanding how and why topology enhances the resilience of such entanglement observables, with immediate relevance to the distribution of information through entanglement in noisy environments, such as quantum computers and quantum networks.

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  • Skyrmionic topologies do not require the channel to be unitary, only that it be map preserving.

    “Skyrmionic topologies, on the other hand, do not require the channel to be unitary, only that it be map preserving”

    From Topological robustness of optical skyrmions through a real-world free-space link (2026) · cites this paper as [68]

    Section V (page unavailable) supports the point that a channel need not be unitary: Skyrmion topology is preserved when its effect is a smooth deformation of the map. But the paper does not say that merely being “map preserving” suffices; Section IX also requires conditions for the map to define an integer Skyrmion number. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • Several experiments have simulated the effects of these channels on optical skyrmions, with promising results demonstrating possible resilience.

    “Several experiments have simulated the effects of these channels on optical skyrmions, with promising results demonstrating possible resilience (68).”

    From Topological robustness of optical skyrmions through a real-world free-space link (2026) · cites this paper as [68]

  • Map preserving is typically an easier condition to satisfy than unitarity.

    “which is typically an easier condition to satisfy (68).”

    From Topological robustness of optical skyrmions through a real-world free-space link (2026) · cites this paper as [68]

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Metadata

Authors
de Mello Koch, R., Lu, B.-Q., Ornelas, P., Nape, I., & Forbes, A.
Affiliations
  • School of Science, Huzhou University 1 , Huzhou 313000,
  • School of Physics, University of the Witwatersrand 3 , Private Bag 3, Wits 2050,
ORCID
Venue
APL Quantum
Publisher
AIP Publishing
Published
2025-05-19
Volume
2
Issue
2
ISSN
2835-0103
DOI
10.1063/5.0271868
Cited by
20
References
6
Language
en
Licence
creativecommons.org/licenses/by/4.0/ (vor)
Funders
National Natural Science Foundation of China (12405058)

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