Uniqueness and Optimality of Dynamical Extensions of Divergences

Understand

We introduce an axiomatic approach for channel divergences and channel relative entropies that is based on three information-theoretic axioms of monotonicity under superchannels (i.e.

• generalized data processing inequality), additivity under tensor products, and normalization, similar to the approach given recently for the state domain.
• We show that these axioms are sufficient to give enough structure also in the channel domain, leading to numerous properties that are applicable to all channel divergences.
• These include faithfulness, continuity, a type of triangle inequality, and boundedness between the min and max channel relative entropies.