Entropic uncertainty relations in multidimensional position and momentum spaces

TL;DR

This paper derives generalized entropic uncertainty relations for multidimensional quantum states, providing optimal bounds and linking to variance-based principles, with an open conjecture for future exploration.

Contribution

It introduces a twofold generalization of entropic uncertainty relations to multidimensional spaces, offering optimal bounds and connecting to variance-based uncertainty principles.

Findings

Derived new multidimensional entropic uncertainty relations

Provided optimal lower bounds for these relations

Linked entropic bounds to variance-based uncertainty principles

Abstract

Commutator-based entropic uncertainty relations in multidimensional position and momentum spaces are derived, twofold generalizing previous entropic uncertainty relations for one-mode states. They provide optimal lower bounds and imply the multidimensional variance-based uncertainty principle. The article concludes with an open conjecture.