Heisenberg’s uncertainty principle, the limits to knowledge, and the foundations of quantum theory

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This project will establish what the uncertainty principle can teach us about quantum foundations, and will address why quantum theory obeys such a principle and why Nature chose quantum theory amongst other possible theories. Specifically, this project will determine how the uncertainty principle restricts the information one can get on incompatible measurements, by deriving new complementarity relations. These will clarify what can or cannot be done in the context of quantum information. This project will determine how much of a theory can be reconstructed from such relations and what other fundamental axioms are required to fully derive quantum theory. This will shed light on the reasons why Nature prefers it to other theories.