Proofs of network quantum nonlocality aided by machine learning

Entanglement and the Path Integral

“…The violation of the resulting "triangle-locality" condition (for certain fixed values of u; see [5,14] for details) therefore proves either nonlocality (direct influences between disconnected worldlines) or else some explanation of hidden correlations which violate Eqn. ( 27).…”

Inflation: a Python library for classical and quantum causal compatibility

“…A particularly successful tool is the inflation method [20][21][22], which consists of a series of increasingly strict necessary conditions that can be tested via linear or semidefinite programming. Despite its broad applicability within and outside the field of quantum nonlocality, available implementations of the inflation technique are typically limited in terms of the type of causal structures it applies to, or in the type of inflations considered (see, e.g., [23,24]). This means that researchers must code their own programs every time they seek to analyze a different structure or try a different solution, adding an extra level of difficulty to the application of the technique.…”

“…After this, the user can specify either a probability distribution over the visible nodes for a feasibility problem (i.e., to determine whether the distribution can be identified as incompatible with the causal structure) using the function set_values(), or a combination of operators whose expectation value will be optimized, by using the function set_objective(). When using set_values(), the user can choose to set also the so-called linearized polynomial constraints, which constrain the set of compatible distributions further at the expense of obtaining certificates with more limited applicability [24,40].…”

“…Linearized polynomial constraints are used, for instance, in Ref. [24] in the case of inflation for compatibility with classical models. For compatibility with quantum models, [40, App.…”

Towards a minimal example of quantum nonlocality without inputs

“…1. While the example of Fritz can be viewed as an embedding of the well-known CHSH Bell test in the triangle network (see also [14]), more recent work by Renou et al [15], followed by other examples [16][17][18][19], suggested that a different form of quantum nonlocality without inputs can be also observed. Here, no obvious connection to standard Bell nonlocality can be made, suggesting a form of quantum nonlocality genuine to this network structure, as further examined in Ref.…”