1 Department of Computer Science, Science and Technology, Aarhus University2 Department of Mathematics, ETH Zurich3 Center for Quantum Technologies, National University of Singapore4 Institute for Theoretical Physics, ETH Zurich5 Department of Computer Science, Science and Technology, Aarhus University
The chain rule for the Shannon and von Neumann en- tropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here, we consider the chain rule for the more general smooth min- and max-entropies, used in one-shot in formation theory. For these en- tropy measures, the chain rule no longer holds as an equality. How- ever, the standard chain rule for the von Neum ann entropy is re- trieved asymptotically when evaluating the smooth entropies for many identical and independently distributed states.
I E E E Transactions on Information Theory, 2013, Vol 59, Issue 5, p. 2603-2612
Chain rules; one-shot information theory; Smooth entropy