Joint Range of R\'enyi Entropies

TL;DR

This paper characterizes the precise range of possible values for multiple Rényi entropies simultaneously, using topological methods to understand their bounds without explicit formulas.

Contribution

It introduces a topological approach to determine the exact range of joint Rényi entropies, extending prior work limited to two entropies.

Findings

Determined the exact range of multiple Rényi entropies.

Developed a topological method for analyzing entropy bounds.

Provided insights into the structure of Rényi entropy space.

Abstract

The exact range of the joined values of several R\'{e}nyi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied. Like in the case when only two orders of R\'{e}nyi entropies are studied one can parametrize upper and lower bounds but an explicit formula for a tight upper or lower bound cannot be given.