Structures from Quantum Relations

Dec 16 11:00 ₂₀₂₂

Abstract: The category of relations and the category of complex linear maps have a lot in common. In particular, they are both compact closed. More concretely, in the same way that any classical process can be characterized by its set of admissible behaviours, any quantum process can be characterized by one vector, a quantum state over all observable behaviours. Thus, complex vectors can be thought of as the quantum generalization of the concept of relations. In this talk, I will illustrate this quantum relation paradigm with two examples. First, I will present a model of quantum wang tiles able to represent quantum configurations obeying local constraints. Then I will outline applications to the semantics of quantum processes via a model of generalized proof nets. Finally, I will provide arguments for the extension of those approaches beyond the quantum realm.