Relating different quantum generalizations of the conditional Rényi entropy

Relating different quantum generalizations of the conditional Renyi entropy

Marco Tomamichel,1, 2 Mario Berta,3, 4 and Masahito Hayashi5, 1 Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore School of Physics, The University of Sydney, Sydney 2006, Australia Institute for Quantum Information and Matter, Caltech, Pasadena, CA 91125, USA Institute for Theoretical Physics, ETH Zurich, 8092 Zürich, Switzerland Graduate School of ...

A Preferred Definition of Conditional Rényi Entropy

The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced a...

On the Conditional Rényi Entropy

Stefan Berens Conditional Rényi entropy

The introduction of the Rényi entropy allowed a generalization of the Shannon entropy and unified its notion with that of other entropies. However, so far there is no generally accepted conditional version of the Rényi entropy corresponding to the one of the Shannon entropy. Different definitions proposed so far in the literature lacked central and natural properties one way or another. In this...

A duality relation connecting different quantum generalizations of the conditional Rényi entropy

Recently a new quantum generalization of the Rényi divergence and the corresponding conditional Rényi entropies was proposed. Here we report on a surprising relation between conditional Rényi entropies based on this new generalization and conditional Rényi entropies based on the quantum relative Rényi entropy that was used in previous literature. This generalizes the well-known duality relation...