Quantum information - flow , concretely , abstractly Bob Coecke

These ‘lecture notes’ are based on joint work with Samson Abramsky. I will survey and informally discuss the results of [3, 4, 5, 12, 13] in a pedestrian not too technical way. These include: • ‘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 defined strongly compact closed categories which abstractly capture the behavioral properties of quantum entanglement. • ‘Postulates for an abstract quantum formalism’ in which classical informationflow (e.g. token exchange) is part of the formalism. As an example, we provided a purely formal description of quantum teleportation and proved correctness in abstract generality. In this formalism types reflect kinds, contra the essentially typeless von Neumann formalism [25]. Hence even concretely this formalism manifestly improves on the usual one. • ‘A high-level approach to quantum informatics’. Indeed, the above discussed work can be conceived as aiming to solve: ??? von Neumann quantum formalism ' high-level language low-level language . I also provide a brief discussion on how classical and quantum uncertainty can be mixed in the above formalism (cf. density matrices). 1 What? When? Where? Why? First of all, for us ‘quantum’ stands for the concepts (both operational and formal) which had to be added to classical physics in order to understand observed phenomena such as ∗Howard Barnum, Rick Blute, Sam Braunstein, Vincent Danos, Ross Duncan, Peter Hines, Martin Hyland, Prakash Panangaden, Peter Selinger and Vlatko Vedral provided feedback. Samson Abramsky and Mehrnoosh Sadrzadeh read this manuscript. 1The identification of quantum information-flow was the content of my QPL I talk. 2This abstract quantum formalism will be presented at LiCS’04 in a joint talk by Samson Abramsky and myself, and also in Samson Abramsky’s invited lecture. 3This will be discussed in Samson Abramsky’s invited lecture at LiCS’04. 4My talk at QPL II will to a great extent cover this particular feature.