Multipartite entanglement detection from correlation tensors

We introduce a general framework for detecting genuine multipartite entanglement and non full-separability in multipartite quantum systems of arbitrary dimensions based on correlation tensors. Regarding genuine multipartite entanglement our conditions are comparable to previous approaches in the case of qubits while they show particular strength in the relatively unexplored case of higher dimensional systems. In the case of non-full separability our conditions prove to be advantageous in situations where more than two-body correlations are relevant, where most previous conditions turned out to be weak. Moreover, they allow for the detection of fully bound entangled states. Finally, we also discuss experimentally-friendly ways of implementing our conditions, which are based on directly measurable quantities.