Unique Information and Secret Key Decompositions

Abstract

The 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 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 two-way secret key rate. We conjecture that the $UI$ lower bounds the two-way rate and discuss implications of the conjecture.

arXiv comment7 pages

References in corpus (6)

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• Reconsidering unique information: Towards a multivariate information decomposition
• Computing the Unique Information
• Unique Informations and Deficiencies
• The Blackwell relation defines no lattice
• Distributions Attaining Secret Key at a Rate of the Conditional Mutual Information