Model-independent inference of quantum interaction from statistics

Any physical theory aims to establish the relationship between physical systems in terms of the interaction between these systems. However, any known approach in the literature to infer this interaction is dependent on the particular modelling of the physical systems involved. Here, we propose an alternative approach where one does not need to model the systems involved but only assume that these systems behave according to quantum theory. We first propose a setup to infer a particular entangling quantum interaction between two systems from the statistics. For our purpose, we utilise the framework of Bell inequalities. We then extend this setup where an arbitrary number of quantum systems interact via some entangling interaction.