[Enlarge image]Left: The joint wavefunction of two entangled photons, A and B, can be engineered to have a nonlocal topology, shown here as a stereographic projection of vectors that cover a sphere. Right: The topology can be used as an infinitely large encoding alphabet, depicted here as the letters A through D as examples corresponding to wrapping numbers of ±1 and ±3.
Topology has long been framed as a mechanism to achieve robustness to noise, in which an underlying feature of the system, characterized by a topological invariant, remains unchanged after certain types of distortion. Recently, optical topologies have emerged1 based on the spatial structure of light,2 but their classical nature has prohibited their application in quantum systems, where information distributed across entangled states must be preserved even when entanglement is fragile. We recently showed that entanglement and topology are inextricably linked, allowing quantum entangled photons to be engineered to hold a nonlocal topology even when each photon locally has no topology. We also illustrated how this leads to preservation of the topology even while the entanglement is decaying.3
Quantum entangled light is an invaluable resource in many applications, from communication and computing to imaging and sensing. But using entanglement when conditions are less than pristine has proved challenging. The traditional approach—trying to preserve entanglement in noisy systems—has had limited success.
As an alternative, could one allow the entanglement to be fragile, and preserve the information instead? Although topology has the potential for information robustness, it had not previously been demonstrated across entangled particles, as the latter would require a new, nonlocal form of topology. The insight to make this possible hinges on the very notion of entanglement, demonstrated in our work with photons.
In the example shown in the accompanying figure, photon A “lives” in a spatial degree of freedom, while photon B “lives” in polarization; the wavefunction is engineered so that a measurement in all space on photon A results in every possible polarization in photon B. We colloquially explain entanglement as a measurement on photon A collapsing the state of photon B to some outcome—an essential feature of nonlocality.
Another way to say this is that, as we cover the full space of photon A, we map to the entire Poincaré sphere of photon B, wrapping the sphere one or more times over. Topology is exactly this—a mapping from one space to another. The topological invariant in this instance is how many times we wrap the sphere of photon B as we measure photon A.
It seems that quantum wavefunctions define the mapping needed for topology. Where is this topology? Intriguingly, it lives in the entanglement between the photons, even though each photon by itself (locally) has no topology. Thus a new nonlocal topology is produced from the very nature of entanglement itself.
The benefit of these nonlocal topologically entangled states is their robustness to perturbations, which we demonstrated experimentally for real-world environments such as background noise and state decay. The new question posed by this advance is whether we can build a toolkit that exploits an infinitely large encoding alphabet based on these topology classes. Addressing this exciting challenge holds the promise of high-capacity quantum information processing and communication that is robust in real-world environments such as global quantum networks and noisy quantum computers.
Researchers
Pedro Ornelas, Isaac Nape and Andrew Forbes, University of the Witwatersrand, Johannesburg, South Africa
Robert de Mello Koch, Huzhou University, Huzhou, China
References
1. Y. Shen et al. Nat. Photonics 18, 15 (2024).
2. A. Forbes et al. Nat. Photonics 15, 253 (2021).
3. P. Ornelas et al. Nat. Photonics 18, 258 (2024).