Entropic uncertainty relation in de Sitter space

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.

Entropic uncertainty relations and their applications

“…Entropic uncertainty relations may play a role in the study of phase transitions in condensed matter physics (Romera and Calixto, 2015). Entropic uncertainty relations are also studied in the context of special and general relativity (Feng et al, 2013;Jia et al, 2015). Given that quantum information is playing an increasing role in cosmology (Hayden and Preskill, 2007), it would not be surprising to see future work on entropic uncertainty relations in the context of black hole physics.…”

Dynamical Measurement's Uncertainty in the Curved Space‐Time

“…[29,30] Additionally, some authors have made many efforts to improve the lower bounds in, [31][32][33][34][35][36] and the uncertainty inequality has been expanded to multipartite systems [37,38] and the stronger entropic uncertainty relations for multiple measurements have been reported. [40][41][42][43][44][45][46][47] Besides, there are also some investigations on the dynamics of QMA-EUR under the noninertial system [48] and the solid-state system. Based on this consideration, it is in demand to understand how the decoherence or dissipation influences the dynamics of the measurement uncertainty.…”

Inhibiting decoherence of two-level atom in thermal bath by presence of boundaries

“…When the atom is far away from the reflecting boundary, i.e., z 0 → ∞, the term 1 − f (ω 0 , z 0 ) → 1 in expressions (23) and (24), and we immediately recover the atom at rest in the unbounded Minkowski case. For the case of the atom is very close to the reflecting boundary ( z 0 → 0), and the atom has parallel dipole polarization, we obtain α z = 0 and f x (ω 0 , z 0 ) = f y (ω 0 , z 0 ) = 1.…”