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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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Dual Objects

Dual Objects

Chapter:
(p.89) 3 Dual Objects
Source:
Categories for Quantum Theory
Author(s):

Chris Heunen

Jamie Vicary

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198739623.003.0003

Dual objects are abstract categorical structures that represent the quantum notion of entanglement. We prove a range of important results about dual objects and show how to use them to model quantum teleportation. Dual objects have an important topological representation, in terms of wires bending ‘backwards in time’, and we use this to characterize different sorts of duality structures, including pivotal, ribbon and compact structures. Dual objects interact well with any linear structure available, allowing us to capture linear-algebraic properties such as trace and dimension.

Keywords:   Dual object, Pivotal category, Ribbon category, Compact category, Trace, Dimension, Teleportation

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