Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotone Measures for Non-Local Correlations   Non-locality is the phenomenon of observing strong correlations among the
outcomes of local measurements of a multipartite physical system. No-signaling
boxes are the abstract objects for studying non-locality, and wirings are local
operations on the space of no-signaling boxes. This means that, no matter how
non-local the nature is, the set of physical non-local correlations must be
closed under wirings. Then, one approach to identify the non-locality of nature
is to characterize closed sets of non-local correlations. Although non-trivial
examples of wirings of no-signaling boxes are known, there is no systematic way
to study wirings. In particular, given a set of no-signaling boxes, we do not
know a general method to prove that it is closed under wirings. In this paper,
we propose the first general method to construct such closed sets of non-local
correlations. We show that a well-known measure of correlation, called maximal
correlation, when appropriately defined for non-local correlations, is
monotonically decreasing under wirings.
  This establishes a conjecture about the impossibility of simulating isotropic
boxes from each other, implying the existence of a continuum of closed sets of
non-local boxes under wirings. To prove our main result, we introduce some
mathematical tools that may be of independent interest: we define a notion of
maximal correlation ribbon as a generalization of maximal correlation, and
provide a connection between it and a known object called hypercontractivity
ribbon; we show that these two ribbons are monotone under wirings too.

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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int