Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Secret Common Information Duality for Tripartite Noisy Correlations   We explore the duality between the simulation and extraction of secret
correlations in light of a similar well-known operational duality between the
two notions of common information due to Wyner, and G\'acs and K\"orner. For
the inverse problem of simulating a tripartite noisy correlation from noiseless
secret key and unlimited public communication, we show that Winter's (2005)
result for the key cost in terms of a conditional version of Wyner's common
information can be simply reexpressed in terms of the existence of a bipartite
protocol monotone. For the forward problem of key distillation from noisy
correlations, we construct simple distributions for which the conditional
G\'acs and K\"orner common information achieves a tight bound on the secret key
rate. We conjecture that this holds in general for non-communicative key
agreement models. We also comment on the interconvertibility of secret
correlations under local operations and public communication.

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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga