Entropic Uncertainty Relations in Quantum Physics

TL;DR

This paper reviews the development and advantages of entropic uncertainty relations in quantum physics, focusing on their generalizations involving Shannon and Rényi entropies and their connection to observable phenomena.

Contribution

It provides a comprehensive overview of entropic uncertainty relations, highlighting their advantages and discussing open problems in the field.

Findings

Entropic uncertainty relations offer a more direct connection to observed quantum phenomena.

Generalizations involving Shannon and Rényi entropies enhance the understanding of quantum uncertainty.

The review identifies key open problems in the development of entropic uncertainty relations.

Abstract

Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the R\'enyi and the Shannon entropies. The advantages of these entropic uncertainty relations are pointed out and their more direct connection to the observed phenomena is emphasized. Several remaining open problems are mentioned