Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower and Upper Conditioning in Quantum Bayesian Theory   Updating a probability distribution in the light of new evidence is a very
basic operation in Bayesian probability theory. It is also known as state
revision or simply as conditioning. This paper recalls how locally updating a
joint state can equivalently be described via inference using the channel
extracted from the state (via disintegration). This paper also investigates the
quantum analogues of conditioning, and in particular the analogues of this
equivalence between updating a joint state and inference. The main finding is
that in order to obtain a similar equivalence, we have to distinguish two forms
of quantum conditioning, which we call lower and upper conditioning. They are
known from the literature, but the common framework in which we describe them
and the equivalence result are new.

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The categories of this paper are: nucl-th
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: hep-ex