In the 20th century, quantum mechanics, along with general relativity, led to redefinitions of the basic principles underlying our understanding of the physical world. Quantum theory is both exciting and puzzling: it has received precise experimental verifications, its mathematical structure is well understood, while none of the attempted causal explanations are fully satisfactory. My research interests are two-fold.
First, to demonstrate the paradigm shift brought by quantum theory, we need to characterize the behavior of various systems respecting the causal relations of classical physics.
Second, quantum systems exhibit novel properties such as entanglement or nonlocality which can be harnessed in a variety of tasks. Suprisingly, we can evaluate those properties from the external behavior of a quantum system, using only minimal assumptions about the underlying causal structure.
To solve these questions, my main focus is on developing practical mathematical and computational tools for the characterization of causal scenarios involving classical and/or quantum resources. For that purpose, I draw tools from discrete probability theory, convex optimization, real algebraic geometry and computational group theory. In particular, the study of symmetries of Bell scenarios proved to be fruitful, and I expect group-theoretical methods to play an important role in other structures.