Tomographic characterization of correlations in a photonic tripartite state

Starting from a four-partite photonic hyper-entangled Dicke resource, we report the full tomographic characterization of three-, two- and one-qubit states obtained by projecting out part of the computational register. The reduced states thus obtained correspond to fidelities with the expected states larger than 87%, therefore certifying the faithfulness of the entanglement-sharing structure within the original four-qubit resource. The high quality of the reduced three-qubit state allows for the experimental verification of the Koashi-Winter relation for the monogamy of correlations within a tripartite state. We show that, by exploiting the symmetries of the three-qubit state obtained upon projection over the four-qubit Dicke resource, such a relation can be experimentally fully characterized using only five measurement settings. We highlight the limitations of such an approach and sketch an experimentally oriented way of overcoming them