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 Gacs and Korner. For the inverse problem of simulating a tripartite noisy correlation from noiseless secret key and unlimited public communication, we show that Winters (2005) result for the key cost in terms of a conditional version of Wyners 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 Gacs and Korner 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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