Emergent particles with nonabelian exchange statistics are a key element in the understanding of topological condensed matter system. However, the nonabelian nature has never been demonstrated experimentally, nor has the intimately connected nonlocality of quantum states been observed in any physical system. With this proposal, we outline a research program whose goal is to design and carry out experiments, with close theoretical coupling, that can – for the first time – verify or falsify the existence of these fascinating novel degrees of freedom and then, if observed, quantify the spatial and temporal limits for the nonabelian and nonlocal properties. The platform for the research is based on topological superconductivity in hybrid materials, a field in which the applicants have played a leading role. We put together a team of experimental and theoretical physicists in a strongly collaborative setup. The focus of the proposal is Majorana bound states, which exist at the boundaries of topological superconductors. Experiments have over the past five years shown observations consistent with their existence. All these experiments are based on local probes which cannot reveal the inner nature of their nonlocal and nonabelian properties. To address the fundamental aspects of nonlocality, we will design quantum devices that combine topological superconductors with known condensed matter quantum technologies, including quantum dots, two-dimensional electron gases, and fast measurement techniques. The nonabelian nature will be explored by design of multi-Majorana devices and of protocols that can reveal the nonabelian nature of braids in the space of topologically-protected groundstate manifolds. The gained knowledge will provide a breakthrough in the fundamentals of emergent degrees of freedom and quantum states encoded in topological macroscopic systems. Their possibly profound character might have future applications in quantum technologies.