260012 UE Modern Foundations of Quantum Mechanics - Exercises (2017W)

Quantum foundations research in the course of the 80 years of the existence of quantum theory has predominately focused on interpreting the theory without ever arriving at a consensus on what its philosophical and epistemological implications are. Through no-go theorems, such as Bell’s theorem or the Kochen-Specker theorem, we now know what quantum mechanics is not, but still quantum researchers cannot seem to agree on what it is. Recently, new research efforts have concentrated on the aim of explaining the physical content of quantum theory by attempting to formulate a set of simple, plausible physical principles from which the theory may be reconstructed. An important aspect of this approach is to view quantum theory within the broader “landscape” of general probabilistic theories. In the current lecture, I will start by presenting traditional and modern no-go theorems for quantum theory and then go on to explain underlying physical ideas and techniques that enable the reconstruction of quantum formalism therefrom.

Topics: Einstein-Podolsky-Rosen paradox, Kochen-Specker theorem, Bell’s theorem, non-local boxes, non-local and no-signalling polytopes, no finite-speed influences, non-extendibility of quantum theory, Pusey-Barrett-Rudolph theorem, no finite information content in a quantum
system, generalized probabilistic theories, reconstructions of quantum theory, quantum theory with no causal order.