  In the early 1960s, inspired by developing notions of topological structure,
Tony Skyrme suggested that sub-atomic particles be described as natural
excitations of a single quantum field. Although never adopted for its intended
purpose, the notion of a skyrmion as a topologically stable field configuration
has proven highly versatile, finding application in condensed matter physics,
acoustics and more recently optics, but all realised as localised fields and
particles. Here we report the first non-local quantum entangled state with a
non-trivial topology that is skyrmionic in nature, even though each individual
photon has no salient topological structure. We demonstrate how the topology of
the quantum wavefunction makes such quantum states robust to entanglement
decay, remaining intact until the entanglement itself vanishes. Our work points
to a nascent connection between entanglement classes and topology, holding
exciting promise for the creation and preservation of quantum information by
topologically structured quantum states that persist even when entanglement is
fragile.
