Rényi Entropy and the Uncertainty Relations

Formulation of the uncertainty relations in terms of the Rényi entropies

Quantum-mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Rényi entropies. The proof of these inequalities requires the use of the exact expression for the p ,q -norm of the Fourier transformation derived by Babenko and Beckner. Analogous uncertainty relations are derived for angle and angular momentum and also for a pair of compl...

A Note on Maximum Rényi Entropy OWA Problem

Uncertainty relations with quantum memory for the Wehrl entropy

We prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. These are the first entropic uncertainty relations with quantum memory ever proposed for a single measurement. The first relation applies to the bipartite memory scenario and provides a lower bound to the Wehrl entropy of a quantum state conditioned on the memory quantum system in terms of the von Neum...

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...

Power law distribution of Rényi entropy for equilibrium systems having nonadditive energy

Using Rényi entropy, an alternative statistics to Tsallis one for nonextensive systems at equilibrium is discussed. We show that it is possible to have the q-exponential distribution function for equilibrium nonextensive systems having nonadditive energy but additive entropy. PACS : 02.50.-r, 05.20.-y, 05.70.-a