A note on entropic uncertainty relations of position and momentum

TL;DR

This paper proposes a new interpolated entropic uncertainty relation for position and momentum measurements, aiming to improve existing bounds, but its validity remains unproven and unrefuted.

Contribution

It introduces a novel interpolation of entropic uncertainty relations for position and momentum, unmentioned in prior literature, as a candidate for an improved inequality.

Findings

Proposes a new interpolation of uncertainty relations

Unverified status of the proposed inequality

Challenges for future validation or falsification

Abstract

We consider two entropic uncertainty relations of position and momentum recently discussed in literature. By a suitable rescaling of one of them, we obtain a smooth interpolation of both for high-resolution and low-resolution measurements respectively. Because our interpolation has never been mentioned in literature before, we propose it as a candidate for an improved entropic uncertainty relation of position and momentum. Up to now, the author has neither been able to falsify nor prove the new inequality. In our opinion it is a challenge to do either one.