Dottorato in FISICA

Titolo della tesi: Causal Inference in Quantum Technologies

In the realm of quantum information and quantum technologies, the fields of statistical inference play a prominent role. These fundamental tools are critical for the study of physical systems in an inherently statistical theory such as quantum mechanics, two notable examples being quantum state and process tomography. Recently causal inference, i.e. the task of discovering causal relationships from experimental data, started to gain attention from the quantum information community. Indeed it has become clear that causal inference provides an excellent framework for the study of the Bell theorem and its generalizations which represent the cornerstone of many applications in quantum information processing. In this thesis, these topics are explored mostly from an experimental point of view, and both fundamental and applied aspects of classical causal modeling in quantum mechanics are explored. On the fundamental side, the works presented here regard mainly the study of non-classicality of complex networks composed of several independent unobserved variables, whose constraints are characterized by a richer structure than simple causal models, and are relevant for the development of quantum communication between several parties over long distances. In particular, it is presented an implementation of a complex quantum network with star and triangle topologies demonstrating experimentally the violation of non-linear causal constraints. Simpler causal structures, like the prepare and measure scenario, are also analyzed. This structure, in particular, is implemented to demonstrate experimentally the non-classicality of a two-dimensional quantum system, in the context of wave-particle duality. On a more theoretical side, a technique is presented which offers a description of causal constraints as an undirected graph, a method already popular in quantum contextuality, which allows to leverage several results from graph theory to analyze causal scenarios. Finally, concerning cryptographical applications, a proof of principle implementation of a certified randomness generator using the instrumental causal structure is described. In the end, the purpose is to show the power of causal modeling applied to quantum mechanics, both for applications and for the foundations of quantum mechanics.