Entropic uncertainty relation of two-qubit detectors coupled to scalar fields in an expanding spacetime

The principles of quantum information provide new avenues to investigate the cosmos. The uncertainty principle is an important trait of the nonclassical world, and it characterizes a significant lower bound (LB) that can be used to estimate measurement results for two noncommuting observables. Subsequently, the uncertainty principle is generalized to a new version by using the entropy and the quantum memory, that is, the quantum-memory-assisted entropic uncertainty relations (Q-M-A-E-U-Rs). Here, considering two qubit detectors coupled to scalar fields, we explore the effects of different cosmic parameters on Q-M-A-E-U-Rs and reveal the influence of the Holevo quantity on the LB of a Q-M-A-E-U-R. It is revealed that an increase in the expansion rapidity of spacetime can enhance the entropic uncertainty and decrease the ability to accurately predict the measurement outcome. The volume expansion leads to the invariance of the entropic uncertainty. An increase in the particle mass of the scalar field causes degradation in entropic uncertainty. In addition, the influence of the Holevo quantity on the Q-M-A-E-U-R’s LB can be ignored if one considers (σx,σy)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\sigma _x},{\sigma _y})$$\end{document} as two complementary observables. Therefore, one can use the Adabi bound and Berta bound to equivalently predict the left-hand side (LHS) of the Q-M-A-E-U-R in this situation. However, when (σx,σz)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\sigma _x},{\sigma _z})$$\end{document} are chosen as two noncommuting observables, the effect of the Holevo quantity on the LB of the uncertainty relation cannot be ignored, and the Adabi bound can always precisely achieve the LHS and predict entropic uncertainty.