We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
104/2019
Unique Information and Secret Key Decompositions
Johannes Rauh, Pradeep Kumar Banerjee, Eckehard Olbrich and Jürgen Jost
The \emph{unique information} ($UI$) is an information measure that quantifies a deviation from the Blackwell order. We have recently shown that this quantity is an upper bound on the \emph{one-way secret key rate}. In this paper, we prove a triangle inequality for the $UI$, which implies that the $UI$ is never greater than one of the best known upper bounds on the \emph{two-way secret key rate}. We conjecture that the $UI$ lower bounds the two-way rate and discuss implications of the conjecture.
