Quantum information-flow, concretely, and axiomatically

Details Quantum information-flow, concretely, and axiomatically Quantum information-flow, concretely, and axiomatically

2005-06-16

arxiv.org/abs/quant-ph/0506132v1

Physics

Quantum Physics

Lecture notes of talks given between Summer 2003 and Spring 2004; they appeared (I guess) as conference proceedings of both QP

Scientific paper

10.1117/12.620297

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'.

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