MiS Preprint Repository

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 ( 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

Unique Informations and Deficiencies

Pradeep Kumar Banerjee, Eckehard Olbrich, Jürgen Jost and Johannes Rauh


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.


Related publications

2018 Repository Open Access
Pradeep Kumar Banerjee, Eckehard Olbrich, Jürgen Jost and Johannes Rauh

Unique informations and deficiencies

In: 2018 56th Annual Allerton Conference on communication, control, and computing
Piscataway, N.J. : IEEE, 2018. - pp. 32-38