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.
CITATION STYLE
Banerjee, P. K. (2015). A secret common information duality for tripartite noisy correlations. In Communications in Computer and Information Science (Vol. 536, pp. 329–341). Springer Verlag. https://doi.org/10.1007/978-3-319-22915-7_31
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