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Genuine Multipartite Entanglement without Multipartite Correlations

Non-classical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are $n$-particle states which do not exhibit $n$-partite correlations at all but still are genuinely $n$-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without $n$-partite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.