Spreading nonlocality in a quantum network

Abstract

Starting from several copies of bipartite noisy entangled states, we design a global and optimal local measurement-based protocol in one- and two-dimensional lattices by which any two or more prefix sites can be connected via entanglement. Production of bipartite as well as multipartite entangled states in a network is verified in a device-independent way through the violation of Bell inequalities with two settings per site and with continuous range of settings. We also note that if the parties refuse to perform local measurements, the entanglement distribution scheme fails. We obtain critical values of noise allowed in the initial state so that the resulting output state show nonlocal correlation in different networks with arbitrary number of connections. We report that by employing our method, it is possible to create a multipartite entangled state, violating Bell inequality and having a continuous range of settings, from bipartite states which do not violate Clauser-Horne-Shimony-Halt Bell inequalities in an one-dimensional lattice with the minimal coordination number being six. Such a feature of superadditivity in violation can also be observed in a triangular two-dimensional lattice but not in a square lattice.