Building a quantum network that links quantum computers is hard because noise from the environment easily disrupts quantum states. Entanglement between distant photons is especially fragile. Once it is lost, quantum state transfer and communication protocols that depend on it stop working. Yet losing entanglement does not necessarily mean that every nonclassical feature of a quantum state disappears.
An international team led by Professor Liang Feng at the University of Pennsylvania has now experimentally confirmed that, by exploiting topology, certain geometric features can persist after the entanglement between photons has vanished. The results appeared on October 12, 2026 in the paper "Chip-mediated manipulation of photonic quantum skyrmions" in Nature Physics (DOI: 10.1038/s41567-026-03487-x), and on October 30 the University of Pennsylvania announced the research.
Using a silicon nitride (Si₃N₄) nanophotonic chip, the team transferred the topology of a polarization structure called a "quantum skyrmion," formed on a single photon, into a quantum state shared by two entangled photons. They then added controlled noise until the entanglement disappeared. The topological invariant describing the winding of the polarization structure was maintained up to a certain noise level.
This does not mean "unbreakable quantum communication" has been achieved. What persisted was a topological feature of a specific quantum state. The result does not guarantee that arbitrary quantum information can be recovered without error, nor that information-transfer performance improves in practical communication channels. The significance of the work lies in experimentally clarifying the relationship between topology and quantum correlations other than entanglement, and in suggesting a new possibility for protecting quantum information.
Quantum Skyrmions and Topology Encoded in Light's Polarization
Skyrmions are special structures originally known in condensed matter physics. In magnetic materials, they appear as tiny magnetic structures in which electron spins are arranged in a vortex-like pattern. The orientation of neighboring spins changes gradually, forming a geometric pattern as a whole. A hallmark of this structure is that even if individual spin orientations change somewhat, the overall winding does not change easily.
The "quantum skyrmion" in this study is neither a spin arrangement in matter nor light physically traveling in a vortex. It is a "spin texture" (polarization structure), describing how the polarization state of a photon is distributed in space, designed to have the same mathematical properties as a skyrmion. Polarization states can be expressed as three-dimensional vectors using quantities called Stokes parameters. The direction of this vector changes regularly across the spatial distribution of the light, and the design forms a specific winding structure.
The structure is characterized by an integer-valued topological invariant, the "skyrmion number." It is determined by how many times the distribution of the Stokes vector covers the surface of the Poincaré sphere, which represents polarization states. For example, a skyrmion number of 2 means the polarization structure covers the Poincaré sphere twice. Just as the number of holes in a doughnut does not change when it is smoothly deformed, the skyrmion number is preserved as long as the topology does not change, even if the polarization vector distribution varies continuously.
The key point is that local changes in polarization and changes in the topology of the whole structure do not necessarily coincide. Even if a photon is disturbed and part of its polarization state changes, the overall winding number stays the same as long as the change remains a continuous deformation. But if noise becomes strong enough that the vector field defining the polarization structure reaches a singular state, the topology itself can change. The stability of the skyrmion is therefore not unlimited; the question is how much noise it can withstand while keeping its structure.
In quantum information processing, entanglement between distant photons is an important resource. In protocols such as quantum teleportation, degraded shared entanglement lowers the fidelity of state transfer, and if entanglement is completely lost, state transfer based on it cannot work. Quantum states, however, also contain nonclassical correlations beyond entanglement. This study examined how far skyrmion topology is maintained as entanglement between photons is lost.
Transferring Topology from One Photon to Two on a Silicon Nitride Chip
The experiment used a silicon nitride photonic integrated circuit fabricated at the Singh Center for Nanoscale Technology at the University of Pennsylvania. A 310 nm silicon nitride layer was formed on a silicon oxide substrate, and optical waveguides, microring resonators, interferometers and other components were integrated. The chip combines several functions: photon pair generation, path control and skyrmion structure formation. The experiment was conducted in a controlled optical setup, not as a demonstration over a telecom operator's fiber installed outdoors.
Photon pairs were generated using a nonlinear optical effect called spontaneous four-wave mixing (SFWM). Femtosecond laser pulses were sent into two spiral waveguides on the chip, producing photon pairs entangled in path. The photons were separated by wavelength-division elements and guided to different paths by an array of Mach-Zehnder interferometers (MZIs) using the thermo-optic effect. This makes it possible to form a skyrmion structure on one photon while controlling the entanglement of the pair.
To write the skyrmion structure onto a single photon, the team used a special microring resonator that couples spin and orbital angular momentum (OAM). Fine periodic structures on the inside and outside of the resonator generate light components with different polarization states and orbital angular momenta, and these are superposed. This creates a quantum state in which the photon's polarization and spatial mode are linked. The structure mainly studied had a theoretical skyrmion number of 2.
The key capability the team demonstrated is the transfer of the topology of this local skyrmion on a single photon into a nonlocal quantum state shared by two photons. Specifically, they performed a Bell state measurement (BSM) on the polarization and momentum of photon A, and achieved transfer of the quantum state according to the measurement result. The transferred skyrmion structure is characterized by the quantum correlation between the orbital angular momentum of photon A and the polarization of photon B. In other words, a topological feature localized on one photon was moved into a configuration shared as a correlation between two photons.
Previous studies had reported forming skyrmion structures on single photons and giving entangled photon pairs nonlocal skyrmion structures. What distinguishes this work is that it demonstrates a mechanism for transferring topology from a single photon to a shared two-photon state on a reconfigurable photonic integrated circuit. It shows that not only can a quantum state be generated, but its topological properties can be manipulated between different quantum states.
Quantum states were evaluated with quantum state tomography (QST), which reconstructs a density matrix from multiple measurement results. Tomography uses combinations of different measurement bases and accumulates photon coincidence counts to estimate the state. Under the measurement conditions given in the manuscript, 16 projective measurements were performed, with 3 minutes of photon-count data acquired for each. Counts in complementary measurement bases totaled about 500, and time-correlated single-photon counting (TCSPC) was used to examine correlations in photon arrival times.
According to the Nature Physics paper, the initially formed single-photon skyrmion state had a fidelity of 86% ± 2% to the ideal target state and a skyrmion number of 1.981 ± 0.002. In the preparation stage of the entangled photon pair, the fidelity reached 91% ± 2%. The following values were also reported for the four Bell state measurement results after topology transfer.
| Measured quantum state | Fidelity | Skyrmion number |
|---|---|---|
| Initial single-photon skyrmion | 86% ± 2% | 1.981 ± 0.002 |
| Two-photon state after transfer ① | 87% ± 3% | 1.981 ± 0.001 |
| Two-photon state after transfer ② | 88% ± 3% | 1.981 ± 0.001 |
| Two-photon state after transfer ③ | 89% ± 2% | 1.979 ± 0.001 |
| Two-photon state after transfer ④ | 89% ± 2% | 1.9798 ± 0.0009 |
The theoretical skyrmion number is 2. The four post-transfer states represent results distinguished by Bell state measurement. Values are based on the measurement results in the Nature Physics paper.
In every transfer result, the skyrmion number was extremely close to the theoretical value of 2. Although the fidelities carry some error, the topological winding structure was maintained with high accuracy. The team stresses that the skyrmion number obtained in the transferred quantum state is reconstructed from quantum correlations between two photons, not from a classical optical polarization pattern. However, these fidelities indicate agreement with the target quantum state and do not directly indicate transmission efficiency or data rates of a communication channel.
Skyrmion Number Persisted Even After Entanglement Vanished
Having confirmed the topology transfer from one photon to two, the team next examined how the quantum state changes when noise is added. In the experiment, they introduced incoherent white-light noise with adjustable background and intensity, creating an environment close to an ideal depolarizing channel. A depolarizing channel is a model in which a quantum state gradually approaches a mixed state due to noise. It does not reproduce every disturbance in real optical fiber links, but it is useful for comparing the effects of noise on quantum correlations and topology.
As noise increased, the fidelity of the two-photon state fell and the off-diagonal elements of the density matrix shrank. Concurrence, which expresses the strength of entanglement, also fell and eventually reached zero. Concurrence is a measure of entanglement between two qubits on a scale from 0 to 1, where 0 means no entanglement and 1 means maximal entanglement. At this stage, the resource needed for ordinary entanglement-based quantum state transfer has been lost.
Yet when the skyrmion number was calculated from the same quantum state, the topological feature was still maintained after concurrence reached zero. The paper shows that entanglement disappears when the parameter γ, which represents the purity of the quantum state, drops below about 0.34, while the skyrmion number continues to stay close to the theoretical value of 2 over a certain range. Even after entanglement between the photons was lost, the global winding number of the polarization structure did not immediately vanish.
In four representative states measured at varying noise levels, the skyrmion number changed as 1.981 ± 0.001, 1.97 ± 0.01, 1.93 ± 0.08 and 0.002 ± 0.001. A value of about 2 was maintained as noise increased from the initial stage, while the last state dropped to nearly zero. Because the topology also collapses once noise exceeds a certain threshold, this phenomenon is not unconditional robustness but threshold-dependent topological stability.
| Metric | What it measures | Change as noise increases | What it does not guarantee |
|---|---|---|---|
| Entanglement (Concurrence) | Quantum entanglement between two photons | Falls with increasing noise and reaches zero at a threshold | Loss of entanglement does not mean all nonclassical correlations are lost |
| Skyrmion number | Global winding number of the polarization structure | Maintained after entanglement vanishes, then collapses sharply under stronger noise | Complete transmission or recovery of arbitrary quantum information |
| Quantum discord | Nonclassical quantum correlations not limited to entanglement | Remains nonzero after entanglement vanishes and decreases with increasing noise | Success of quantum computation or communication without error correction |
In the theoretical model, as γ approaches about 0.25, mixing by noise overwhelms the original quantum state and the skyrmion number also collapses to zero. This is because the Stokes vector field degenerates and can no longer maintain its earlier winding structure. That the threshold for losing entanglement differs from the threshold for topological collapse shows that the two do not measure the same property of the quantum state.
The team also examined how closely the noise introduced in the experiment approximates an ideal depolarizing model. A density matrix reconstructed solely from noise-derived coincidence counts showed a fidelity of 98.4% to the theoretical maximally mixed state. This is consistent with noise acting almost isotropically, but it does not mean a perfectly ideal depolarizing channel was formed. In the experiment, the decline in fidelity and skyrmion number began slightly earlier than theoretically predicted, and the team suggests the influence of residual anisotropic noise.
The paper also tested robustness not only to isotropic noise but to anisotropic quantum noise corresponding to phase flip and bit-phase flip. In these tests, noise channels were simulated by combining phase manipulation on the photonic chip with numerical mixing of measurement results. The skyrmion number was shown to be maintained until the parameters corresponding to phase-flip and bit-phase-flip probabilities approached 0.5. The robustness tests were therefore not limited to isotropic white-light noise, but they did not evaluate all of the complex noise found in real communication channels.
Caution is also needed about measurement uncertainty. The error ranges in the paper are one standard deviation (1σ) obtained from 100 Monte Carlo simulations, assuming photon counts follow Poisson statistics. They therefore do not cover all systematic errors inherent to the experimental setup, such as slight misalignment of optical elements, detector dark counts and long-term instrument drift. Evaluating practical noise tolerance will require separating such statistical errors from instrument-related systematic errors.
Quantum Discord Reveals Correlations Beyond Entanglement, and Hurdles to Practical Use
To explore why the skyrmion number was maintained after entanglement vanished, the team calculated "quantum discord" from the two-photon density matrix. Quantum discord captures a broader range of quantum correlations than entanglement and relates to how much the correlations of a quantum state change under local measurement. Even for a separable quantum state with no entanglement, quantum discord is not necessarily zero. Because of this property, it is used to investigate nonclassical correlations that entanglement alone cannot capture.
Analysis of the experimental data showed that quantum discord maintained a nonzero value even in the region where concurrence was zero. This means nonclassical correlations remain in the quantum state after entanglement is lost. The team believes these remaining correlations play an important role in maintaining the skyrmion's winding structure. The interpretation is that even when noise alters the quantum state, the skyrmion number is conserved as long as the structure remains topologically equivalent to the original state.
Furthermore, analysis of the quantum channel model built by the team shows that states in which skyrmion topology is maintained are accompanied by nonzero quantum discord. However, this relationship runs in one direction: nonzero quantum discord does not necessarily mean the skyrmion number is maintained. In fact, there are regions where quantum discord remains even after the topology has collapsed. Maintaining the skyrmion number therefore implies not merely that quantum correlations exist, but that those correlations preserve a specific spatial structure.
This result adds a new perspective to evaluating the noise tolerance of quantum states using entanglement as the sole indicator. The skyrmion number may serve as a topological indicator capturing nonclassical correlations that remain after entanglement is gone. However, while the persistence of quantum discord was shown to be linked to this phenomenon, that alone does not establish a practical mechanism for protecting quantum information.
The team points to possible applications of such topological properties in future quantum interconnects, technology for linking distant quantum processors or quantum computers with light and exchanging quantum information. If topological features in a quantum state are stable against noise, they could offer new options for encoding and transferring information in distributed quantum computing. But what this experiment demonstrated is the transfer and retention of a specific topological invariant, not a practical performance improvement in quantum state transfer itself.
At a minimum, the following points will need to be verified for practical use.
- Application to actual quantum information transmission: Beyond simply measuring the skyrmion number, it must be shown that information can be encoded using the topological structure and read out correctly at the receiver. Cryptographic protocols such as quantum key distribution (QKD) have not actually been run, and information-theoretic security has not been demonstrated.
- Robustness over long-distance channels: Whether topological features can be maintained over tens of kilometers of optical fiber or free-space propagation through the atmosphere remains unconfirmed. In real channels, dispersion, polarization mode dispersion (PMD) and polarization-dependent loss (PDL) act in combination, so effects may differ from the noise simulated in the laboratory.
- Recovery of arbitrary quantum states and error correction: Maintaining the skyrmion number does not mean the amplitude and phase information of an arbitrary qubit can be fully preserved. It must be confirmed whether lost quantum information can be recovered and whether there are concrete benefits when combined with existing quantum error correction schemes.
Going forward, in addition to independent replications using different wavelengths and substrate materials, it will be important to see whether the topological properties are reproduced in complex noise environments closer to real communication channels. A major focus will be whether information can be encoded, transmitted and decoded using topological structure under conditions where entanglement is lost. A large gap remains between maintaining some features of a quantum state and being able to communicate arbitrary quantum information.
This study provides foundational knowledge for bridging that gap. Its significance lies in showing experimentally that, even after entanglement vanishes, nonclassical correlations typified by quantum discord, and the topological structure tied to them, are maintained under certain conditions. Whether this property can be used for actual information transmission is an important question for future research.