Conditional quantum entropy from information-theoretic principles

Sarah Brandsen, Duke University, North Carolina

In this work, we introduce an axiomatic approach for characterising quantum conditional entropy which relies on only two key axioms. More specifically, we demonstrate that any function satisfying monotonicity under conditionally unital and semicausal channels as well as additivity for product channels is sufficient to guarantee negativity of the function for maximally entangled states. These two axioms are additionally sufficient to demonstrate that conditional entropy is non-negative for separable bipartite states. Finally, we develop an operational approach for characterising entropy via games of chance, and show that this approach yields the same ordering as the axiomatic approach in the case where the bipartite states are classical.