Abstract: Topological phases of matter cannot be detected locally, instead requiring nonlocal probes. In this talk, we will explore two different experimental set-ups where these 'nonlocal' features appear. The first is an analog Bose-Hubbard quantum simulator, based on an ongoing collaboration with the Greiner lab [Su et al, to appear]. The arguably simplest example of topological matter appears upon introducing a staggered chemical potential. This provides an ideal platform to study quantum criticality between topologically distinct phases, where we observe an even-odd effect when stacking copies of the system as well as mixed-state order due to stability against disorder. In the second part of the talk, we turn to a digital realization of a qutrit version of the toric code on Quantinuum's trapped-ion quantum processor [Iqbal et al, arxiv:2411.04185]. We observe the transfer of entanglement between anyons and non-abelian defects, which serves as a precursor to a universal gate-set achievable in future experiments on a closely-related non-abelian topologically ordered state.