Entropic Uncertainty Relations In Curved Spacetime

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) SV{Q|A)+SV(R|A)> log2 1/C+Su(B|A), which de-notes the uncertainty of outcomes of simultaneously measuring two incompatible observables Q and R.In this paper, 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 in-trinsic thermal nature of the de Sitter space and the Unruh effect associated with the proper acceleration of A also brings effect on entropic uncertainty. Through straightforward calculation and analysis, we conclude that the higher the temper-ature is, the greater the uncertainty is and the quicker the uncertainty reaches the maxima value.And finally the possible mechanism behind this phenomenon is also explored from the perspective of quantum correlation. We find the decrease of quantum cor-relation may make the outcomes of two incompatible observables more uncertain and the lower bound lifted. When the quantum correlation eventually vanishes, the uncertainty arrives at a maxima value. And the increase of temperature makes the quantum correlation smaller, and the uncertainty becomes greater.