Contradictory uncertainty relations

TL;DR

This paper demonstrates that different measures of quantum uncertainty, such as Tsallis and Renyi entropies, can lead to conflicting conclusions about minimum and maximum uncertainty states within a simple framework.

Contribution

It reveals that various entropic uncertainty relations can produce contradictory results, highlighting the complexity of defining quantum uncertainty.

Findings

Tsallis and Renyi entropic uncertainty relations can yield opposite uncertainty state conclusions

Minimum uncertainty states in one relation may be maximum in a related relation

Conflicting results depend on the measure of fluctuations used

Abstract

We show within a very simple framework that different measures of fluctuations lead to uncertainty relations resulting in contradictory conclusions. More specifically we focus on Tsallis and Renyi entropic uncertainty relations and we get that the minimum uncertainty states of some uncertainty relations are the maximum uncertainty states of closely related uncertainty relations, and vice versa.