Entropic time-energy uncertainty relations: An algebraic approach

TL;DR

This paper develops algebraic methods to derive entropic time-energy uncertainty relations, providing improved bounds in certain scenarios and introducing a versatile approach applicable to various entropic uncertainty principles.

Contribution

It introduces a novel algebraic approach to derive entropic uncertainty relations between time and energy, improving previous bounds and broadening applicability.

Findings

Improved entropic uncertainty bounds for specific guessing games.

Introduction of a new algebraic method for deriving uncertainty principles.

Applicability of the method to a wider class of entropic relations.

Abstract

We address entropic uncertainty relations between time and energy or, more precisely, between measurements of an observable $G$ and the displacement $r$ of the $G$-generated evolution $e^{-ir G}$. We derive lower bounds on the entropic uncertainty in two frequently considered scenarios, which can be illustrated as two different guessing games in which the role of the guessers are fixed or not. In particular, our bound for the first game improves the previous result by Coles et al.. Our derivation uses as a subroutine a recently proposed novel algebraic method, which can in general be used to derive a wider class of entropic uncertainty principles.