Quantum information-flow, concretely, and axiomatically

Abstract

These lecture notes survey some joint work with Samson Abramsky. Somewhat informally I will discuss the main results in a pedestrian not too technical way. These include: (1) `The logic of entanglement', that is, the identification and abstract axiomatization of the `quantum information-flow' which enables protocols such as quantum teleportation. To this means we define strongly compact closed categories which abstractly capture the behavioral properties of quantum entanglement. (2) `Postulates for an abstract quantum formalism' in which classical information-flow (e.g. token exchange) is part of the formalism. As an example, we provide a purely formal description of quantum teleportation and prove correctness in abstract generality. In this formalism types reflect kinds, contra the essentially typeless von Neumann formalism. Hence even concretely this formalism manifestly improves on the usual one. (3) `A high-level approach to quantum informatics'.