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Quantum Information Processing

, Volume 15, Issue 12, pp 5179–5209 | Cite as

Categories of quantum and classical channels

  • Bob Coecke
  • Chris Heunen
  • Aleks Kissinger
Article

Abstract

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.

Keywords

Abstract C*-algebras Categorical quantum mechanics   Completely positive maps Quantum channel 

Mathematics Subject Classification

81P45 16B50 18D35 46L89 46N50 81P16 

Notes

Acknowledgments

This research was supported by the Engineering and Physical Sciences Research Council Fellowship EP/L002388/1, and the John Templeton Foundation.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of OxfordOxfordUK

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