  An open challenge in the context of quantum information processing and
communication is improving the robustness of quantum information to
environmental contributions of noise, a severe hindrance in real-world
scenarios. Here we create quantum skyrmionic topologies across two degrees of
freedom in two entangled photons and show that the topological invariant
remains resilient even as the purity of the state decreases due to
environmental noise, collapsing only once the state is maximally mixed. We
discuss how such noise perturbations can be considered a smooth deformation of
the state, and provide a full theoretical treatment to support the experimental
findings. Our approach can be viewed as a digitization of quantum information,
holding exciting promise for intrinsic quantum resilience through topology.
