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. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft