Unique Information and Secret Key Decompositions
This work addresses fundamental limits in secure communication for cryptography, but it appears incremental as it builds on prior bounds and conjectures without experimental validation.
The paper tackles the problem of bounding secret key rates in information theory by proving a triangle inequality for the unique information measure, which shows it does not exceed a known upper bound on the two-way secret key rate, and conjectures it may lower bound this rate.
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.