Higher dimensional entanglement without correlations

It has been demonstrated both theoretically and experimentally that genuine multipartite entanglement between qubits can exist even in the absence of multipartite correlations. Here we provide first examples of this effect in higher dimensional systems -- qudits. We construct states in which genuine $N$-partite entanglement between qudits is supported only by correlations involving strictly less than $N$ particles. The construction differs in several aspects from the ones for qubits. The states introduced here are a natural test-bed for candidate quantifiers of genuinely multipartite quantum correlations.