Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unentangled Measurements and Frame Functions   Gleason's theorem asserts the equivalence of von Neumann's density operator
formalism of quantum mechanics and frame functions, which are functions on the
pure states that sum to 1 on any orthonormal basis of Hilbert space of
dimension at least 3. The unentangled frame functions are initially only
defined on unentangled (that is, product) states in a multi-partite system. The
third author's Unentangled Gleason's Theorem shows that unentangled frame
functions determine unique density operators if and only if each subsystem is
at least 3-dimensional. In this paper, we determine the structure of
unentangled frame functions in general. We first classify them for multi-qubit
systems, and then extend the results to factors of varying dimensions including
countably infinite dimensions (separable Hilbert spaces). A remarkable
combinatorial structure emerges, suggesting possible fundamental
interpretations.

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The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas