Entropic uncertainty relation in de Sitter space

TL;DR

This paper investigates how the entropic uncertainty relation in quantum mechanics is influenced by the thermal effects of de Sitter space, revealing that higher temperatures increase uncertainty.

Contribution

It analyzes the impact of de Sitter space's thermal nature on the entropic uncertainty relation using an open quantum system approach, considering both free-fall and static observers.

Findings

Thermal bath from Gibbons-Hawking temperature increases uncertainty.

Higher temperature leads to greater and faster-reaching uncertainty.

Intrinsic and Unruh-related temperatures affect the entropic uncertainty.

Abstract

The uncertainty principle restricts our ability to simultaneously predict the measurement outcomes of two incompatible observables of a quantum particle. However, this uncertainty could be reduced and quantified by a new Entropic Uncertainty Relation (EUR). By the open quantum system approach, we explore how the nature of de Sitter space affects the EUR. When the quantum memory $A$ freely falls in the de Sitter space, we demonstrate that the entropic uncertainty acquires an increase resulting from a thermal bath with the Gibbons-Hawking temperature. And for the static case, we find that the temperature coming from both the intrinsic thermal nature of the de Sitter space and the Unruh effect associated with the proper acceleration of $A$ also brings effect on entropic uncertainty, and the higher temperature, the greater uncertainty and the quicker the uncertainty reaches the maxima value. And finally the possible mechanism behind this phenomenon is also explored.