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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.
Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the secret. Thus,
We develop a connection between tripartite information $I_3$, secret sharing protocols and multi-unitaries. This leads to explicit ((2,3)) threshold schemes in arbitrary dimension minimizing tripartite information $I_3$. As an application we show tha
A source model of key sharing between three users is considered in which each pair of them wishes to agree on a secret key hidden from the remaining user. There are rate-limited public channels for communications between the users. We give an inner b
We consider the problem of decomposing the total mutual information conveyed by a pair of predictor random variables about a target random variable into redundant, unique and synergistic contributions. We focus on the relationship between redundant i
It is well known that physical-layer key generation methods enable wireless devices to harvest symmetric keys by accessing the randomness offered by the wireless channels. Although two-user key generation is well understood, group secret-key (GSK) ge