Relating different quantum generalizations of the conditional Renyi entropy

2013/11/30 by Marco Tomamichel, Mario Berta, Masahito Hayashi · 2 citations
Physics and Astronomy · Computer Science · Mathematics · #quant-ph #cs.IT #math.IT

paper · pdf · doi:10.1063/1.4892761

published as J. Math. Phys. 55 (8), 082206 (2014) · 10 pages, 1 figure

arxiv created 2014/08/15 · arxiv updated 2014/08/18

Abstract

Recently a new quantum generalization of the Renyi divergence and the corresponding conditional Renyi entropies was proposed. Here we report on a surprising relation between conditional Renyi entropies based on this new generalization and conditional Renyi entropies based on the quantum relative Renyi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Renyi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Renyi entropies and derive a new entropic uncertainty relation.

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