New entropic uncertainty relations for prime power dimensions

TL;DR

This paper derives improved entropic uncertainty relations for prime power dimensional quantum systems by establishing a tight classical bound on entropy under collision probability constraints, linking classical info theory to quantum uncertainty.

Contribution

It introduces a new classical bound on entropy with fixed collision probabilities and connects it to quantum entropic uncertainty relations in prime power dimensions.

Findings

Derived a tight lower bound on entropy for multiple distributions.

Connected classical bounds to quantum entropic uncertainty relations.

Enhanced understanding of uncertainty relations in higher-dimensional quantum systems.

Abstract

We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple probability distributions under the constraint that the sum of the collision probabilities for all distributions is fixed. This is purely a classical information theoretical result, however using an interesting result by Larsen \cite{Larsen90} allows us to connect this to an entropic uncertainty relation.