Entropic uncertainty minimum for angle and angular momentum

Abstract

Uncertainty relations are key components in the understanding of the nature of quantum mechanics. In particular, entropic relations are preferred in the study of angular position and angular momentum states. We propose a new form of angle–angular momentum state that provides, for all practical purposes, a lower bound on the entropic uncertainty relation, , for any given angular uncertainty, thus improving upon previous bounds. We establish this by comparing this sum with the absolute minimum value determined by a global numerical search. These states are convenient to work with both analytically and experimentally, which suggests that they may be of use for quantum information purposes.

On quantum states for angular position and angular momentum of light

“…In the course of the present work we have found that less general expressions than equations ( 9) and ( 14) have been discussed in the literature in the context of a minimum entropic angular position and angular momentum quantum states [40].…”