Basis-independent coherence and its distribution in de Sitter spacetime

TL;DR

The paper tackles how basis-independent quantum coherence behaves for two Unruh–DeWitt detectors in de Sitter spacetime, revealing how curvature and horizon-induced thermality shape quantum resources. It develops a Markovian open-system framework, analyzes detectors in both Bunch–Davies and $\alpha$-vacua, and decomposes coherence into total, collective, localized, and global components using Jensen–Shannon-based measures. A key finding is that vacuum squeezing in $\alpha$-vacua can substantially enhance extractable coherence, especially the genuinely non-local global coherence $C_G$, even in the presence of thermal noise from the Gibbons–Hawking effect; the coherence distribution shows clear decoupling between local and non-local mechanisms. The results provide a robust, observer-independent toolkit for relativistic quantum information tasks in curved spacetime and offer insights into managing quantum resources in cosmological settings.

Abstract

Quantum coherence in curved spacetime offers a fresh window into the interplay between gravity, thermality, and quantum resources. While previous work has shown that Markovian evolution can generate entanglement and other nonclassical correlations in de Sitter backgrounds, the basis-dependent nature of coherence has so far limited its unambiguous interpretation. Here, we introduce a basis-independent framework to quantify not only the total coherence of two comoving detectors, but also its collective and localized contributions, and we trace how each of these decomposed measures varies with the inverse of Gibbons-Hawking temperature. By treating the detectors as open quantum systems interacting with a massless scalar field in the Bunch-Davies and squeezed alpha-vacua, we find that non-thermal squeezing substantially enhances extractable coherence, even under strong thermal effects. Our results demonstrate how basis-independent coherence in de Sitter spacetime can serve as a robust resource for relativistic quantum information protocols.

Figures (3)

• Figure 1: The total $C_T$\ref{['figure1a']}, collective $C_C$\ref{['figure1b']}, localized $C_L$\ref{['figure1c']}, and global coherence $C_G$\ref{['figure1d']} associated with the state $\eta(t)$ describing the UDW detectors in de Sitter space, plotted versus $\beta$ for selected magnitudes of $|\alpha|$ with $\omega=1.5$, and $\tau=0.9$.
• Figure 2: The total $C_T$\ref{['figure2a']}, collective $C_C$\ref{['figure2b']}, localized $C_L$\ref{['figure2c']}, and global coherence $C_G$\ref{['figure2d']} associated with the state $\eta(t)$ describing the UDW detectors in de Sitter space, plotted versus $\beta$ for chosen values of $\omega$ with $\left| \alpha\right|=2$, and $\tau=0.9$.
• Figure 3: The total $C_T$\ref{['figure3a']}, collective $C_C$\ref{['figure3b']}, localized $C_L$\ref{['figure3c']}, and global coherence $C_G$\ref{['figure3d']} associated with the state $\eta(t)$ describing the UDW detectors in de Sitter space, as a function of $\tau$ and $\alpha$ with $\omega=3$, and $\beta=1$.