Triangle Nonlocality : genuine quantum nonlocality and quantum Finner inequality*

Network nonlocality extends standard Bell nonlocality to networks, where several independent sources are distributed to several parties according to the network structure. Contrary to standard Bell Nonlocality, this problem is non convex: no efficient systematic way to tackle it is known, either for local or quantum correlations. It is only partially understood for the simplest scenarios of bilocality (extended to star-locality and nonlocality on a line). However, for scenarios with loops, e.g. the triangle network, nothing is known except examples directly deduced from the usual form of quantum nonlocality (via the violation of a standard Bell inequality). This can even be done without using inputs. The question of finding a genuine quantum violation of triangle network locality was open the last years.
In this talk, we first present a novel example of quantum nonlocality without inputs in the triangle network, which we believe represent a new form of quantum nonlocality, genuine to the triangle network. It involves both entangled qubit states and joint entangled measurements. We generalize it to qutrits shared states and any odd-cycle networks.
Then, we move to the question of the characterization of local and quantum correlations. We derive a bound, the quantum Finner inequality (already known to hold for local ressources), which we also demonstrate to hold when the sources are arbitrary no-signaling boxes which can be wired together. We generalizes this bound to all networks involving bipartite sources. We discuss it as an application for the device-independent characterization of the topology of a quantum network.
We conclude with some open questions related to quantum network nonlocality.
This talk is based on the two letters arXiv:1905.04902 and arXiv:1901.08287