A novel chain rule for one-shot entropic quantities via operational methods
Sayantan Chakraborty, Upendra Kapshikar · 2023
We introduce a new operational technique for deriving a chain rule for general information theoretic quantities. This technique is very different from the popular (and in some cases fairly involved) methods like SDP formulation and operator algebra or norm interpolation. Instead, our framework considers a simple information transmission task and obtains lower and upper bounds for it. The lower bounds are obtained leveraging a successive cancellation encoding and decoding technique. Pitting the upper and lower bounds against each other gives us the desired chain rule. As a demonstration of this technique we derive the chain rule for the smooth-Hypothesis testing mutual information.The full version of this paper can be found online, see [CK].