Multipartite Nonlocality in Clifford Networks

The rapid development of the theory and experimental realization of quantum networks makes it essential to characterize the features and limitations of different kinds of networks. The limitations of Clifford quantum information processing have been explored both in the sense of classical simulability under the light of the Gottesman-Knill theorem, and of the emergence of quantum nonlocality in specific scenarios. However, it has remained relatively unexplored in a quantum network setting - that is, with limited connectivity and no communication of global information.

Our main result is that networks limited strictly to pure stabilizer states and Clifford gates cannot generate network nonlocality. We prove this by constructing a local model that reproduces the statistics of these Clifford networks. Additionally, we show that (a) Bipartite entanglement can generate all forms of N-party network nonlocality using post-selection, including those that can be achieved by measuring across k-partite (k<N) entangled states; and (b) Different kinds of nonlocality can be achieved by making different relaxations on our Clifford network model.

This work serves as a guide for identifying the resources needed to produce different forms of nonlocality. It also sheds new light on the broader question of what types of networks can generate disguised Bell nonlocality, as opposed to genuine network nonlocality, by showing that all known approaches for generating the latter require some form of non-Clifford operation.