Skyrmions were originally conceived by Tony Skyrme in the 1960s as solitonic solutions of nonlinear field theories, particle-like knots in a continuous field whose identity is fixed by an integer topological charge. In magnetic materials, ultracold atomic gases, liquid crystals and even acoustic systems, these whirls of spin have been studied intensively because their topology protects them against small perturbations, making them attractive carriers of information. In optics, skyrmions have been built from the interplay of polarisation and spatial structure, with the Stokes parameters of a paraxial beam mapping the transverse plane onto the Poincaré sphere. What remained elusive was a quantum version in which the topology itself is not merely a static property of a prepared state but a dynamic, remotely addressable feature of an entangled system.

The new experiment begins with a deceptively simple quantum state. Photon A carries only polarisation, existing in a superposition of right- and left-circular states, while photon B carries one of two possible skyrmion states, each a non-separable combination of the photon’s polarisation and its orbital angular momentum, the twisted spatial structure described by Laguerre-Gaussian modes. Crucially, photon B on its own is described by a mixture of these skyrmion states, so no well-defined spin texture or skyrmion number exists until a measurement is made on photon A. Only when the polarisation of the partner photon is projected does the topology of photon B crystallise into a definite skyrmion with a definite topological number. The researchers describe this arrangement as a non-local quantum dial for topological structure.

To map this dial, the team introduced a conceptual tool they call the topological Bloch sphere. Whereas a conventional Bloch sphere parametrises the states of a two-level quantum system, this new sphere has basis vectors that are themselves topological states, so every point on the sphere corresponds to a different superposition of the two skyrmion states and therefore to a different Bell state, carrying its own skyrmion number. At the poles of the sphere, where the projections select the basis states, the polarisation texture forms a higher-order skyrmion. Along the equator, where the two basis states are combined in superposition, the texture breaks apart into multiple localised quasiparticles, each with its own skyrmion number, whose individual contributions sum to the total wrapping number of the field.

Experimentally, the photons were generated by spontaneous parametric downconversion in a nonlinear crystal, producing pairs entangled in orbital angular momentum at two different wavelengths, 1550 nanometres and 810 nanometres, separated by a dichroic mirror. Electrically tunable q-plates, liquid-crystal devices with azimuthally varying optical axes, then transformed the orbital-angular-momentum-entangled state into the desired spin-skyrmion entangled tripartite state, with the q-plate charge tailoring the accessible skyrmion sectors. Spatial light modulators, waveplates and single-mode fibres coupled to avalanche photodiodes completed the apparatus, with coincidences recorded within a half-nanosecond window.

The verification was rigorous. A violation of the Clauser-Horne-Shimony-Holt Bell inequality confirmed the non-local character of the correlations, with Bell parameters of 2.53 plus or minus 0.005 and 2.47 plus or minus 0.004 for the two heralded states, both beyond the classical bound of two. A full quantum state tomography, comprising six polarisation projections on the heralding photon and twenty-one combined measurements on the skyrmion photon, reconstructed the density matrix with a fidelity of 0.93 and a purity of 0.96. From the reconstructed state the team extracted the spatially varying Stokes parameters and computed the skyrmion number directly, observing the expected switching between topological sectors: for one configuration the number moved between approximately minus two at the poles and minus four at the equator, and for a second, generated with higher-charge q-plates, between approximately minus three and minus six, in each case matching theory to within a few percent.

The most visually striking outcome is the dynamics. By continuously varying the amplitude and phase angles of the polarisation projection on photon A, the researchers watched the localised quasiparticles of photon B’s multiskyrmion move. Changing the amplitude angle drove the quasiparticles radially, drawing them in from infinity toward the central distribution as the angle increased, until near the pole of the sphere they merged with the central skyrmion and could no longer be resolved as separate objects. Changing the phase angle instead set the quasiparticles orbiting around the centre, while each also exhibited a local spin arising from the precession of its Stokes vector. The symmetry of the distribution governed the total angles traversed: the two-quasiparticle configuration completed one orbit and one spin rotation per full phase scan, while the threefold-symmetric configuration completed an orbit of two-thirds of a full turn and a spin of four-thirds of a turn.

Beneath the spectacle lies a deeper point about multipartite entanglement. By constraining photon B to two of its three spatial modes, the team isolated an embedded GHZ-like state, the tripartite analogue of a Bell pair, in which the polarisation of photon A, the polarisation of photon B and one orbital angular momentum mode of photon B form the familiar pattern of a GHZ state. Projecting photon A onto its basis states collapses the remainder into separable states with trivial topology, while superposition projections collapse it into Bell states encoded in the spin and orbital angular momentum of photon B, each visible as a distinct skyrmionic texture with the same skyrmion number but a different spatial pattern. The Bell-state structure of the embedded GHZ state thus becomes something one can literally see in the polarisation field of a single photon.

The implications stretch toward quantum technology. Because the evolving skyrmionic structure of one photon can serve as a probe of its entangled partner, any perturbation acting on the partner can be read out as a transition between topological sectors or as a subtle shift in the quasiparticle dynamics, suggesting a route to quantum sensing in which complex channel features are mapped onto robust topological observables. The non-degenerate, dual-wavelength implementation adds versatility, allowing topological control at one technologically convenient wavelength while the topology is used or detected at another, with prospects including nonlinear quantum transport and the remote transfer of skyrmionic topology to matter. The authors also envision sharing such states across quantum networks, granting a resource-scarce partner access to complex topological structures that would otherwise be beyond their experimental reach, and exploiting the multipartite state complexity for multi-level quantum communication encoding.

What began six decades ago as an abstract field-theoretic construction has now become a controllable, moving, quantum-mechanical object of light, steered from afar by nothing more than the choice of measurement made on a distant entangled photon. In turning the topology of light into a remote-controlled dial, the researchers have not only made entanglement visible in an entirely new way but have opened a laboratory in which the particle-like textures of quantum fields can be engineered, animated and ultimately put to work.

Subject of Research: Remote control of quantum skyrmion topologies in entangled photon states to visualise tripartite entanglement dynamics

Article Title: Remote engineering of particle-like topologies to visualise entanglement dynamics

Article References: Nothlawala, F., Sephton, B., Ornelas, P., Koni, M., Piccirillo, B., Feng, L., Nape, I., D’Ambrosio, V., & Forbes, A. (2026). Remote engineering of particle-like topologies to visualise entanglement dynamics. Light: Science & Applications, 15(1), Article 368. https://doi.org/10.1038/s41377-026-02443-x

Image Credits: AI Generated

DOI: 10.1038/s41377-026-02443-x

Keywords: skyrmions, quantum entanglement, quantum photonics, orbital angular momentum, topological Bloch sphere, GHZ states, Bell inequality, structured light, quantum state tomography, q-plates, quantum sensing, multiskyrmions

The framework builds on a tradition that stretches back over a century. In the 1920s, Theodor Kaluza and Oskar Klein showed that adding a compact, curled-up fifth dimension to general relativity could reproduce electromagnetism when the extra dimension is projected away. The key insight, echoed across higher-dimensional theories ever since, is that projection from a richer space into a smaller one discards information, and that discarded information can manifest as effective properties, forces, and behaviors that have no direct counterpart in the underlying description. Barros extends this logic to the heart of quantum theory. Physical states, in the new model, live on a five-dimensional manifold consisting of standard spacetime multiplied by a compact circle, parametrized by an angular coordinate that runs from zero to two pi. Observable states are obtained by integrating over this hidden angle, a projection that acts on probability amplitudes rather than probabilities, thereby preserving phase coherence across the compact dimension.

The mathematical heart of the proposal lies in a simple but powerful observation: the projection operator is non-injective, meaning that many distinct higher-dimensional configurations map onto the same observable state. The author proves a proposition showing that a projected bipartite state factorizes into independent parts only under highly constrained conditions, namely when the dependence on the compact coordinate itself separates multiplicatively between the two subsystems. Generically, this condition fails. When it fails, the projected state is non-factorizable: it becomes entangled. In other words, correlations between distant particles emerge as a structural consequence of dimensional reduction, even though the underlying higher-dimensional state was perfectly separable. Entanglement, in this picture, is not a primitive ingredient of reality but an effective phenomenon, akin to how an effective electromagnetic force emerges in Kaluza-Klein theory from pure geometry.

The most striking demonstration of the mechanism is the construction of a Bell state from scratch. Barros considers a two-level system, such as photon polarization with horizontal and vertical states, and writes down a state in the extended space that is manifestly separable: each subsystem carries its own coherent superposition with phases that depend on the hidden angular coordinate. When the projection is applied, the Fourier structure of the compact dimension does the rest. Terms in the tensor product carrying nonzero phase harmonics, such as factors of e to the two-i-theta, integrate to zero by the orthogonality of Fourier modes. Only the phase-neutral terms survive, and after normalization the resulting observable state is exactly the maximally entangled Bell state, with horizontal-horizontal and vertical-vertical components in equal superposition. The interference along the hidden circle, followed by dimensional reduction, manufactures entanglement from a state that possessed none.

Crucially, the framework is not merely a reinterpretation of existing quantum mechanics; it makes testable predictions. When phase cancellation along the compact dimension is incomplete, characterized by a small parameter eta, the projected state acquires additional components that modify the observable correlations. The standard quantum prediction for maximally entangled states is that the correlation function depends only on the difference between the two measurement angles, giving the familiar cosine of a minus b. In the modified framework, an extra term proportional to the cosine of a plus b appears, weighted by a parameter epsilon that measures the residual influence of higher-dimensional modes. This is a qualitatively distinct signature. Ordinary experimental imperfections, such as reduced visibility, simply rescale the standard cosine dependence, whereas the projection-induced term has a different angular structure entirely, meaning that sufficiently precise measurements can in principle distinguish the two.

The author shows that the deviation parameter epsilon could be extracted directly from experiment. By choosing measurement settings such that the standard quantum contribution vanishes, for example with analyzer angles separated by three quarters of pi, the correlation function reduces to exactly epsilon, allowing a single measurement to reveal the presence or absence of higher-dimensional effects. More generally, the full two-parameter angular landscape of correlations can be mapped and fitted to separate the cosine of a minus b from the cosine of a plus b contributions. The statistical requirements are demanding but well within reach of modern photonic platforms. Resolving a deviation of one percent at the three-sigma confidence level requires roughly one hundred thousand detected coincidence events, while a four percent deviation needs only about ten thousand. State-of-the-art Bell experiments routinely achieve pair-generation rates and interference visibilities above ninety-nine percent, placing such measurements squarely within current technological capability.

An important conceptual point is that the model does not fall afoul of Bell’s theorem. The compact coordinate is not an accessible classical hidden variable that predetermines individual measurement outcomes, which is the scenario that Bell’s theorem and its experimental tests rule out. Instead, the projection acts coherently on probability amplitudes, and the resulting correlations remain incompatible with the CHSH bound: the author demonstrates that for the standard optimal measurement settings, the epsilon-dependent contribution cancels exactly in the CHSH combination, so the inequality remains violated throughout the parameter domain. The apparent nonlocality of quantum correlations is thus reinterpreted as an effective phenomenon. Observers confined to the projected spacetime see correlations that cannot be explained locally, while the underlying higher-dimensional description remains local through its dependence on a shared compact coordinate. No superluminal signaling is required, and the framework remains compatible with the no-signalling principle, since the correlations are fixed by the global projected state before any measurement takes place.

The work is explicitly limited to a kinematic level, describing the structure of states and their projection without yet specifying how the higher-dimensional state evolves in time. The author sketches a natural dynamical extension, in which a Hamiltonian defined on the extended space induces effective evolution in the observable domain through the projection operator, potentially explaining the origin of unitary quantum dynamics in geometric terms. Whether the harmonic structure along the compact dimension remains stable under such dynamics, preserving the phase-coherent mode pairs on which the entanglement mechanism depends, is identified as a central open problem for future work. A complete derivation of the effective evolution equation, and a quantitative comparison of the predicted epsilon bounds with the uncertainties of existing high-precision Bell experiments, remain to be carried out.

Even in its present form, the proposal carries considerable conceptual weight. It suggests that several hallmark features of quantum theory, from interference to entropy to entanglement, might share a common geometric origin in the non-injective mapping between a higher-dimensional description and its observable projection. If future experiments detect a nonzero epsilon, it would constitute direct evidence that observable correlations retain imprints of degrees of freedom beyond standard spacetime, a result that would rank among the most profound discoveries in physics. Conversely, increasingly stringent experimental bounds on epsilon would constrain the class of admissible higher-dimensional states, turning the framework into a progressively sharper instrument for probing the geometry underlying quantum mechanics. Either outcome advances the centuries-old project of understanding why the quantum world looks the way it does, and whether the strangeness of entanglement is a fundamental law or, as this work suggests, a shadow cast by dimensions we cannot see.

Subject of Research: Emergence of quantum entanglement from geometric projection of higher-dimensional states

Article Title: Emergent quantum entanglement from higher-dimensional geometric projection

Article References: Barros, A. K. (2026). Emergent quantum entanglement from higher-dimensional geometric projection. Results in Physics, Article 108761. https://doi.org/10.1016/j.rinp.2026.108761

Image Credits: AI Generated

DOI: 10.1016/j.rinp.2026.108761

Keywords: quantum entanglement, higher dimensions, Kaluza-Klein theory, Bell inequality, quantum foundations, dimensional projection, compact dimension, CHSH bound, photonic experiments, quantum correlations, nonlocality, theoretical physics