Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completely positive maps within the framework of direct-sum
  decomposition of state space   We investigate completely positive maps for an open system interacting with
its environment. The families of the initial states for which the reduced
dynamics can be described by a completely positive map are identified within
the framework of direct-sum decomposition of state space. They includes not
only separable states with vanishing or nonvanishing quantum discord but also
entangled states. A general expression of the families as well as the Kraus
operators for the completely positive maps are explicitly given. It
significantly extends the previous results.

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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin