Unique Informations and Deficiencies
This work addresses a theoretical problem in information theory for researchers studying mutual information decompositions, but it appears incremental as it builds on existing concepts like deficiencies and unique information measures.
The paper tackles the problem of measuring unique information between two channels conveying information about the same random variable by introducing two new measures based on generalized weighted Le Cam deficiencies, and relates these to an existing measure called minimum-synergy unique information, providing an operational interpretation in terms of an upper bound on the one-way secret key rate.
Given two channels that convey information about the same random variable, we introduce two measures of the unique information of one channel with respect to the other. The two quantities are based on the notion of generalized weighted Le Cam deficiencies and differ on whether one channel can approximate the other by a randomization at either its input or output. We relate the proposed quantities to an existing measure of unique information which we call the minimum-synergy unique information. We give an operational interpretation of the latter in terms of an upper bound on the one-way secret key rate and discuss the role of the unique informations in the context of nonnegative mutual information decompositions into unique, redundant and synergistic components.