Categories of quantum and classical channels

Bob Coecke, Chris Heunen, Aleks Kissinger

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)5179–5209
Number of pages31
JournalQuantum Information Processing
Issue number12
Early online date15 Oct 2014
Publication statusPublished - Dec 2016

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