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.