Quantum superchannels on the space of quantum channels
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Date
2023-06-20
Authors
Daly, Padraig Conor
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Quantum channels, defined as completely-positive and trace-preserving maps on
matrix algebras, are an important object in quantum information theory. In this thesis
we are concerned with the space of these channels. This is motivated by the study
of quantum superchannels, which are maps whose input and output are quantum
channels.
Rather than taking the domain to be the space of all linear maps, as has been
done in the past, we motivate and define superchannels by considering them as transformations on the operator system spanned by quantum channels. Extension theorems for completely positive maps allow us to apply the characterisation theorem
for superchannels to this smaller set of maps. These extensions are
non unique, showing two different superchannels act the same on all input quantum
channels, and so this new definition on the smaller domain captures more precisely
the action of superchannels as transformations between quantum channels. The non
uniqueness can affect the auxilliary dimension needed for the characterisation as well
as the tensor product of the superchannels.
Description
Keywords
quantum channels, operator systems, quantum information