Distribution and Generation of Quantum Coherence for Gaussian States in de Sitter Space

Abstract

The distribution and generation of quantum coherence for two‐mode and multi‐mode Gaussian states in de Sitter space are studied. It is found that the quantum coherence is redistributed among the mode in different open charts under the curvature effect of de Sitter space. In particular, the Gaussian coherence for the initially correlated state is found to survive in the limit of infinite curvature, while quantum entanglement vanishes in this limit. Unlike entanglement and steering, the coherence of a massive scalar field is more robust than a massless field under the influence of curvature of de Sitter space. In addition, it is shown that the curvature generates two‐mode Gaussian state and three‐mode Gaussian state quantum coherence among the open charts, even though the observers are localized in causally disconnected regions. It is worth noting that the gravity‐generated three‐mode coherence is extremely sensitive to the curvature effect for the conformal and massless scalar fields, which may be in principle employed to design an effective detector for the space curvature.

Black-box estimation of expanding parameter for de Sitter universe

“…In Fig. 2 (b), we can see that both the GIP and entanglement are monotone increasing functions of the curvature parameter p. Considering that the effect of the curvature becomes stronger when p becomes less and less from 1 to 0 [31][32][33][34][35][36], this in fact demonstrates that the lower the space curvature, the higher the accuracy of parameter estimation. It is worth noting that the values of the GIP and entanglement are more sensitive to the spacetime curvature in the massless scalar limit ν = 3/2.…”

“…where σ = ±1 distinguish the independent solutions for each open chart and P ±ip , where p is a positive real parameter normalized by H. The mass parameter ν is defined by ν = 9 4 − m 2 H 2 . Note that the curvature effect starts to appear around p ∼ 1 in three-dimensional hyperbolic space [31][32][33][34][35][36], and the effect of the curvature becomes stronger when p is less than 1. Therefore, p can be considered as the curvature parameter of the de Sitter space.…”