The hidden topology in orbital angular momentum entanglement

We harness orbital angular momentum (OAM) to discover a rich tapestry of topological maps in high dimensional spaces, moving beyond spin textured fields with mixed degrees of freedom to topologies using only the OAM of light. We confirm this experimentally using quantum states with an underlying topology of 48 dimensions and a topological spectrum spanning over 17000 maps, an encoding alphabet with enormous potential. We show that the topological spectrum allows the simultaneous ability to be robust to and probe for perturbation, the latter made possible by observing emergent signatures in the non-topological (trivial) spaces of the spectrum. We outline how our work opens exciting future possibilities for quantum sensing and communications.