Bounding the set of classical correlations of a many-body system

Understand

We present a method to certify the presence of Bell correlations in experimentally observed statistics, and to obtain new Bell inequalities.

• Our approach is based on relaxing the conditions defining the set of correlations obeying a local hidden variable model, yielding a convergent hierarchy of semidefinite programs (SdP's).
• Because the size of these SdP's is independent of the number of parties involved, this technique allows to characterize correlations in many-body systems.
• As an example, we illustrate our method with the experimental data presented in [Science 352, 441 (2016)]