2004/02/18 by Samson Abramsky, Bob Coecke · 1 voice · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #cs.LO #math-ph #math.CT #math.MP #quant-ph
published as Proceedings of the 19th IEEE conference on Logic in Computer Science (LiCS'04). IEEE Computer Science Press (2004) · Significant additions and modifications as compared to the previous version (abstract inner-products, simplified presentation of abstract quantum mechanics). 21 pages, some pictures, some diagrams. 2007 replacement: source had become incompatible with Paul taylor's latest update of his Diagrams package so update was needed
arxiv published 2004/02/18 · arxiv created 2007/03/05 · arxiv updated 2007/03/05
We study quantum information and computation from a novel point of view. Our approach is based on recasting the standard axiomatic presentation of quantum mechanics, due to von Neumann, at a more abstract level, of compact closed categories with biproducts. We show how the essential structures found in key quantum information protocols such as teleportation, logic-gate teleportation, and entanglement-swapping can be captured at this abstract level. Moreover, from the combination of the --apparently purely qualitative-- structures of compact closure and biproducts there emerge `scalars` and a `Born rule'. This abstract and structural point of view opens up new possibilities for describing and reasoning about quantum systems. It also shows the degrees of axiomatic freedom: we can show what requirements are placed on the (semi)ring of scalars C(I,I), where C is the category and I is the tensor unit, in order to perform various protocols such as teleportation. Our formalism captures both the information-flow aspect of the protocols (see quant-ph/0402014), and the branching due to quantum indeterminism. This contrasts with the standard accounts, in which the classical information flows are `outside' the usual quantum-mechanical formalism.