Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Nearly Quantum Theories   We consider possible non-signaling composites of probabilistic models based
on euclidean Jordan algebras. Subject to some reasonable constraints, we show
that no such composite exists having the exceptional Jordan algebra as a direct
summand. We then construct several dagger compact categories of such
Jordan-algebraic models. One of these neatly unifies real, complex and
quaternionic mixed-state quantum mechanics, with the exception of the
quaternionic "bit". Another is similar, except in that (i) it excludes the
quaternionic bit, and (ii) the composite of two complex quantum systems comes
with an extra classical bit. In both of these categories, states are morphisms
from systems to the tensor unit, which helps give the categorical structure a
clear operational interpretation. A no-go result shows that the first of these
categories, at least, cannot be extended to include spin factors other than the
(real, complex, and quaternionic) quantum bits, while preserving the
representation of states as morphisms. The same is true for attempts to extend
the second category to even-dimensional spin-factors. Interesting phenomena
exhibited by some composites in these categories include failure of local
tomography, supermultiplicativity of the maximal number of mutually
distinguishable states, and mixed states whose marginals are pure.

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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci