Entropic uncertainty relation in de Sitter space

• The uncertainty principle could be reduced and quantified by a new Entropic Uncertainty Relation (EUR).
• By the open quantum system approach, we explore how the nature of the de Sitter (dS) space affects the EUR.
• For freely falls case, the entropic uncertainty acquires an increase resulting from the intrinsic thermal nature of the dS space.
• For static case, both the intrinsic thermal nature of the dS space and the Unruh effect brings effect on entropic uncertainty.
• The higher the temperature, the greater the uncertainty and the quicker the uncertainty reaches its maxima value.

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 AA 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 AA also brings effect on entropic uncertainty, and the higher the temperature, the greater the uncertainty and the quicker the uncertainty reaches the maximal value. And finally the possible mechanism behind this phenomenon is also explored.