Complementarity, Incompatibility, and Irreversible Disturbance. A Resolution to the Debate Between Bohr and Heisenberg

In 1927, Heisenberg introduced a heuristic argument, based on the famous γ-ray microscope Gedankenexperiment, to show that in quantum theory there exist operations that irreversibly disturb the systems on which they act. This argument was intended to show the existence of quantities that cannot be simultaneously measured. However, with a deeper understanding of how information can be manipulated and propagated, it is possible to prove that only the converse relation actually holds. In this thesis, exploiting the framework of the framework of Operational Probabilistic Theories (OPTs), we show that the impossibility of performing certain measurements simultaneously implies the existence of operations that irreversibly disturb the systems on which they act. We also present two toy theories, called Minimal Classical Theory (MCT) and Minimal Strongly causal Bilocal Classical Theory (MSBCT), that serve as counterexamples to the converse implication. Even though both theories satisfy full compatibility of observations, they still display irreversibility. Moreover, they are classical, Kochen-Specker, and generalised-noncontextual, yet nonetheless satisfy two quantum no-go theorems: No-Information Without Disturbance (NIWD) and no-broadcasting. This shows that these properties cannot be taken per se as signatures of non-classicality. We also introduce two new classes of operational theories, which we here define and study: Minimal Operational Probabilistic Theories (MOPTs) and Minimal Strongly causal Operational Probabilistic Theories (MSOPTs), of which MCT and MSBCT are representatives, respectively. These theories are characterised by allowing only the minimal possible set of dynamics, with the latter also admitting classical conditioning. We prove that all MOPTs and all MSOPTs whose state spaces contain a spanning set of entangled states necessarily satisfy both NIWD and no-broadcasting. Finally, we propose an operational definition of Bohr’s complementarity, understood as the existence of properties of physical systems that cannot be simultaneously well-defined. We show that complementarity implies incompatibility and, consequently, irreversibility. In the specific case of quantum theory, however, complementarity and incompatibility are proved to coincide.