Uniform continuity bound for sandwiched Rényi conditional entropy

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...

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...

On the Conditional Rényi Entropy

Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints

We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible form that depends only on the system dimension and the trace distance of the states. Almost the same proof can be used to derive similar continuity bounds for t...

An Upper Bound for Uniform Entropy Numbers

Let r > 1 and let Q be a probability measure on a measurable space (X, .4). In this note, we present a proof of a useful bound in Lr ( Q)-norm for the entropy of a convex hull in the case that covering numbers for a class of measurable functions are polynomial.