2013/05/16 by Bob Coecke, Coecke, Bob, Chris Heunen +3 · 5 citations
Physics and Astronomy · Mathematics · Computer Science · #Quantum Mechanics and Applications #Advanced Operator Algebra Research #Quantum Information and Cryptography
paper · pdf · doi:10.48550/arxiv.1305.3821
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of finite-dimensional C*-algebras and completely positive maps. In particular, the new category contains both quantum and classical channels, providing elegant abstract notions of preparation and measurement. We also consider nonstandard models, that can be used to investigate which notions from algebraic quantum information theory are operationally justifiable.