Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Categories of Quantum and Classical Channels (extended abstract)   We introduce the CP*-construction on a dagger compact closed category as a
generalisation of Selinger's CPM-construction. While the latter takes a dagger
compact closed category and forms its category of "abstract matrix algebras"
and completely positive maps, the CP*-construction forms its category of
"abstract C*-algebras" and completely positive maps. This analogy is justified
by the case of finite-dimensional Hilbert spaces, where the CP*-construction
yields the category of finite-dimensional C*-algebras and completely positive
maps.
  The CP*-construction fully embeds Selinger's CPM-construction in such a way
that the objects in the image of the embedding can be thought of as "purely
quantum" state spaces. It also embeds the category of classical stochastic
maps, whose image consists of "purely classical" state spaces. By allowing
classical and quantum data to coexist, this provides elegant abstract notions
of preparation, measurement, and more general quantum channels.

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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: stat