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Categories for Quantum TheoryAn Introduction$
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Chris Heunen and Jamie Vicary

Print publication date: 2019

Print ISBN-13: 9780198739623

Published to Oxford Scholarship Online: January 2020

DOI: 10.1093/oso/9780198739623.001.0001

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Complete Positivity

Complete Positivity

Chapter:
(p.225) 7 Complete Positivity
Source:
Categories for Quantum Theory
Author(s):

Chris Heunen

Jamie Vicary

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198739623.003.0007

Completely positive maps give a notion of quantum process that allows the description of probabilistic effects in quantum theory. We show how to describe this categorically in terms of the CP construction and contrast the behaviour of classical and quantum information in this setting. We also study the behaviour of duality and linear structure under the CP construction.

Keywords:   Completely positive map, CP construction, Stinespring dilation, Kraus map, Ancilla, Environment structure, Decoherence structure

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